%!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: arXiv:cond-mat/0007359v1 [cond-mat.str-el] 24 Jul 2000 %%Pages: 4 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%DocumentFonts: Helvetica Helvetica-Oblique Symbol Times-Italic %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -R -P pk -K1 -z paper.dvi -o %DVIPSParameters: dpi=600, compressed, comments removed %DVIPSSource: TeX output 2018.10.29:0955 %%BeginProcSet: texc.pro /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: 8r.enc % @@psencodingfile@{ % author = "S. Rahtz, P. MacKay, Alan Jeffrey, B. Horn, K. Berry", % version = "0.6", % date = "1 July 1998", % filename = "8r.enc", % email = "tex-fonts@@tug.org", % docstring = "Encoding for TrueType or Type 1 fonts % to be used with TeX." % @} % % Idea is to have all the characters normally included in Type 1 fonts % available for typesetting. This is effectively the characters in Adobe % Standard Encoding + ISO Latin 1 + extra characters from Lucida. % % Character code assignments were made as follows: % % (1) the Windows ANSI characters are almost all in their Windows ANSI % positions, because some Windows users cannot easily reencode the % fonts, and it makes no difference on other systems. The only Windows % ANSI characters not available are those that make no sense for % typesetting -- rubout (127 decimal), nobreakspace (160), softhyphen % (173). quotesingle and grave are moved just because it's such an % irritation not having them in TeX positions. % % (2) Remaining characters are assigned arbitrarily to the lower part % of the range, avoiding 0, 10 and 13 in case we meet dumb software. % % (3) Y&Y Lucida Bright includes some extra text characters; in the % hopes that other PostScript fonts, perhaps created for public % consumption, will include them, they are included starting at 0x12. % % (4) Remaining positions left undefined are for use in (hopefully) % upward-compatible revisions, if someday more characters are generally % available. % % (5) hyphen appears twice for compatibility with both % ASCII and Windows. % /TeXBase1Encoding [ % 0x00 (encoded characters from Adobe Standard not in Windows 3.1) /.notdef /dotaccent /fi /fl /fraction /hungarumlaut /Lslash /lslash /ogonek /ring /.notdef /breve /minus /.notdef % These are the only two remaining unencoded characters, so may as % well include them. /Zcaron /zcaron % 0x10 /caron /dotlessi % (unusual TeX characters available in, e.g., Lucida Bright) /dotlessj /ff /ffi /ffl /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef % very contentious; it's so painful not having quoteleft and quoteright % at 96 and 145 that we move the things normally found there to here. /grave /quotesingle % 0x20 (ASCII begins) /space /exclam /quotedbl /numbersign /dollar /percent /ampersand /quoteright /parenleft /parenright /asterisk /plus /comma /hyphen /period /slash % 0x30 /zero /one /two /three /four /five /six /seven /eight /nine /colon /semicolon /less /equal /greater /question % 0x40 /at /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O % 0x50 /P /Q /R /S /T /U /V /W /X /Y /Z /bracketleft /backslash /bracketright /asciicircum /underscore % 0x60 /quoteleft /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o % 0x70 /p /q /r /s /t /u /v /w /x /y /z /braceleft /bar /braceright /asciitilde /.notdef % rubout; ASCII ends % 0x80 /.notdef /.notdef /quotesinglbase /florin /quotedblbase /ellipsis /dagger /daggerdbl /circumflex /perthousand /Scaron /guilsinglleft /OE /.notdef /.notdef /.notdef % 0x90 /.notdef /.notdef /.notdef /quotedblleft /quotedblright /bullet /endash /emdash /tilde /trademark /scaron /guilsinglright /oe /.notdef /.notdef /Ydieresis % 0xA0 /.notdef % nobreakspace /exclamdown /cent /sterling /currency /yen /brokenbar /section /dieresis /copyright /ordfeminine /guillemotleft /logicalnot /hyphen % Y&Y (also at 45); Windows' softhyphen /registered /macron % 0xD0 /degree /plusminus /twosuperior /threesuperior /acute /mu /paragraph /periodcentered /cedilla /onesuperior /ordmasculine /guillemotright /onequarter /onehalf /threequarters /questiondown % 0xC0 /Agrave /Aacute /Acircumflex /Atilde /Adieresis /Aring /AE /Ccedilla /Egrave /Eacute /Ecircumflex /Edieresis /Igrave /Iacute /Icircumflex /Idieresis % 0xD0 /Eth /Ntilde /Ograve /Oacute /Ocircumflex /Otilde /Odieresis /multiply /Oslash /Ugrave /Uacute /Ucircumflex /Udieresis /Yacute /Thorn /germandbls % 0xE0 /agrave /aacute /acircumflex /atilde /adieresis /aring /ae /ccedilla /egrave /eacute /ecircumflex /edieresis /igrave /iacute /icircumflex /idieresis % 0xF0 /eth /ntilde /ograve /oacute /ocircumflex /otilde /odieresis /divide /oslash /ugrave /uacute /ucircumflex /udieresis /yacute /thorn /ydieresis ] def %%EndProcSet %%BeginProcSet: tx8r.enc % 8r.enc (0.6, 1-jul-98, by S. 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Berry) renamed /TeXBase1Encoding [ /.notdef /dotaccent /fi /fl /fraction /hungarumlaut /Lslash /lslash /ogonek /ring /.notdef /breve /minus /.notdef /Zcaron /zcaron /caron /dotlessi /dotlessj /ff /ffi /ffl /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /grave /quotesingle /space /exclam /quotedbl /numbersign /dollar /percent /ampersand /quoteright /parenleft /parenright /asterisk /plus /comma /hyphen /period /slash /zero /one /two /three /four /five /six /seven /eight /nine /colon /semicolon /less /equal /greater /question /at /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O /P /Q /R /S /T /U /V /W /X /Y /Z /bracketleft /backslash /bracketright /asciicircum /underscore /quoteleft /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p /q /r /s /t /u /v /w /x /y /z /braceleft /bar /braceright /asciitilde /.notdef /.notdef /.notdef /quotesinglbase /florin /quotedblbase /ellipsis /dagger /daggerdbl /circumflex /perthousand /Scaron /guilsinglleft /OE /.notdef /.notdef /.notdef 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/odieresis /divide /oslash /ugrave /uacute /ucircumflex /udieresis /yacute /thorn /ydieresis ] def %%EndProcSet %%BeginProcSet: special.pro TeXDict begin /SDict 200 dict N SDict begin /@SpecialDefaults{/hs 612 N /vs 792 N /ho 0 N /vo 0 N /hsc 1 N /vsc 1 N /ang 0 N /CLIP 0 N /rwiSeen false N /rhiSeen false N /letter{}N /note{}N /a4{}N /legal{}N}B /@scaleunit 100 N /@hscale{@scaleunit div /hsc X}B /@vscale{@scaleunit div /vsc X}B /@hsize{/hs X /CLIP 1 N}B /@vsize{/vs X /CLIP 1 N}B /@clip{ /CLIP 2 N}B /@hoffset{/ho X}B /@voffset{/vo X}B /@angle{/ang X}B /@rwi{ 10 div /rwi X /rwiSeen true N}B /@rhi{10 div /rhi X /rhiSeen true N}B /@llx{/llx X}B /@lly{/lly X}B /@urx{/urx X}B /@ury{/ury X}B /magscale true def end /@MacSetUp{userdict /md known{userdict /md get type /dicttype eq{userdict begin md length 10 add md maxlength ge{/md md dup length 20 add dict copy def}if end md begin /letter{}N /note{}N /legal{} N /od{txpose 1 0 mtx defaultmatrix dtransform S atan/pa X newpath clippath mark{transform{itransform moveto}}{transform{itransform lineto} }{6 -2 roll transform 6 -2 roll transform 6 -2 roll transform{ itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll curveto}}{{ closepath}}pathforall newpath counttomark array astore /gc xdf pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack}if}N /txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1 -1 scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub neg 0 TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{noflips{TR pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop 90 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr 1 get neg sub neg 0 TR}if yflip xflip not and{TR pop pop 270 rotate ppr 2 get ppr 0 get neg sub neg 0 S TR}if}ifelse scaleby96{ppr aload pop 4 -1 roll add 2 div 3 1 roll add 2 div 2 copy TR .96 dup scale neg S neg S TR}if}N /cp {pop pop showpage pm restore}N end}if}if}N /normalscale{Resolution 72 div VResolution 72 div neg scale magscale{DVImag dup scale}if 0 setgray} N /psfts{S 65781.76 div N}N /startTexFig{/psf$SavedState save N userdict maxlength dict begin /magscale true def normalscale currentpoint TR /psf$ury psfts /psf$urx psfts /psf$lly psfts /psf$llx psfts /psf$y psfts /psf$x psfts currentpoint /psf$cy X /psf$cx X /psf$sx psf$x psf$urx psf$llx sub div N /psf$sy psf$y psf$ury psf$lly sub div N psf$sx psf$sy scale psf$cx psf$sx div psf$llx sub psf$cy psf$sy div psf$ury sub TR /setpagedevice{pop}N /showpage{}N /erasepage{}N /copypage{}N /p 3 def @MacSetUp}N /doclip{ psf$llx psf$lly psf$urx psf$ury currentpoint 6 2 roll newpath 4 copy 4 2 roll moveto 6 -1 roll S lineto S lineto S lineto closepath clip newpath moveto}N /endTexFig{end psf$SavedState restore}N /@beginspecial{SDict begin /SpecialSave save N gsave normalscale currentpoint TR @SpecialDefaults count /ocount X /dcount countdictstack N}N /@setspecial {CLIP 1 eq{newpath 0 0 moveto hs 0 rlineto 0 vs rlineto hs neg 0 rlineto closepath clip}if ho vo TR hsc vsc scale ang rotate rwiSeen{rwi urx llx sub div rhiSeen{rhi ury lly sub div}{dup}ifelse scale llx neg lly neg TR }{rhiSeen{rhi ury lly sub div dup scale llx neg lly neg TR}if}ifelse CLIP 2 eq{newpath llx lly moveto urx lly lineto urx ury lineto llx ury lineto closepath clip}if /setpagedevice{pop}N /showpage{}N /erasepage{}N /copypage{}N newpath }N /@endspecial{count ocount sub{pop}repeat countdictstack dcount sub{ end}repeat grestore SpecialSave restore end}N /@defspecial{SDict begin} N /@fedspecial{end}B /li{lineto}B /rl{rlineto}B /rc{rcurveto}B /np{ /SaveX currentpoint /SaveY X N 1 setlinecap newpath}N /st{stroke SaveX SaveY moveto}N /fil{fill SaveX SaveY moveto}N /ellipse{/endangle X /startangle X /yrad X /xrad X /savematrix matrix currentmatrix N TR xrad yrad scale 0 0 1 startangle endangle arc savematrix setmatrix}N end %%EndProcSet %%BeginProcSet: hps.pro /HPSdict 20 dict dup begin/braindeaddistill 50 def/rfch{dup length 1 sub 1 exch getinterval}bind def/splituri{dup(#)search{exch pop}{()exch} ifelse dup(file:)anchorsearch{pop exch pop 3 -1 roll pop false}{pop 3 -1 roll exch pop true}ifelse}bind def/lookuptarget{exch rfch dup /TargetAnchors where{pop TargetAnchors dup 3 -1 roll known{exch get true }{pop(target unknown:)print == false}ifelse}{pop pop (target dictionary unknown\012)print false}ifelse}bind def/savecount 0 def/stackstopped{count counttomark sub/savecount exch store stopped count savecount sub 1 sub dup 0 gt{{exch pop}repeat}{pop}ifelse}bind def /tempstring 256 string def/targetvalidate{1 index dup length 255 gt exch dup(/)search{pop pop pop exch pop true exch}{pop}ifelse cvn tempstring cvs token pop pop length 0 ne or not}bind def/targetdump-hook where{pop} {/targetdump-hook{dup mark exch gsave initmat setmatrix{{mark/Dest 4 2 roll targetvalidate{aload pop exch pop/Page 3 1 roll/View exch[exch /FitH exch]/DEST pdfmark}{cleartomark}ifelse}forall}stackstopped pop grestore}bind def}ifelse/baseurl{mark exch 1 dict dup 3 -1 roll/Base exch put/URI exch/DOCVIEW{pdfmark}stackstopped pop}bind def /externalhack systemdict/PDF known def/oldstyle true def/initmat matrix currentmatrix def/actiondict 2 dict dup/Subtype/URI put def /weblinkhandler{dup 3 1 roll mark 4 1 roll/Title 4 1 roll splituri 3 -1 roll dup length 0 gt{cvn/Dest exch 4 2 roll}{pop}ifelse{externalhack{ /HTTPFile exch}{actiondict dup 3 -1 roll/URI exch put/Action exch} ifelse}{externalhack{/HTTPFile exch}{/File exch/Action/GoToR}ifelse} ifelse counttomark 2 sub -1 roll aload pop/Rect 4 1 roll/Border 3 1 roll /Color exch oldstyle{/LNK}{/Subtype/Link/ANN}ifelse gsave initmat setmatrix{pdfmark}stackstopped grestore}bind def/externalhandler where{ pop}{/externalhandler{2 copy{weblinkhandler}exec{/externalhack externalhack not store 2 copy{weblinkhandler}exec{/externalhack externalhack not store/oldstyle false store 2 copy{weblinkhandler}exec{ (WARNING: external refs disabled\012)print/externalhandler{pop pop}bind store externalhandler}{pop pop}ifelse}{pop pop/externalhack externalhack not store}ifelse}{pop pop/externalhandler{weblinkhandler pop}bind store} ifelse}bind def}ifelse/pdfmnew{dup type/stringtype eq{externalhandler}{ exch dup rfch exch 3 -1 roll lookuptarget{mark 4 1 roll/Title 4 1 roll aload pop exch pop/Page 3 1 roll/View exch[exch/FitH exch]5 -1 roll aload pop/Rect 4 1 roll/Border 3 1 roll/Color exch/LNK gsave initmat setmatrix pdfmark grestore}{pop pop}ifelse}ifelse}bind def/pdfmold{dup type/stringtype eq{externalhandler}{exch dup rfch exch 3 -1 roll lookuptarget{mark 4 1 roll/Title 4 1 roll aload pop exch pop/Page 3 1 roll/View exch[exch/FitH exch]5 -1 roll aload pop pop 0 3 getinterval /Rect 3 1 roll/Border exch/LNK gsave initmat setmatrix pdfmark grestore} {pop pop}ifelse}ifelse}bind def/pdfm where{pop}{/pdfm /currentdistillerparams where{pop currentdistillerparams dup /CoreDistVersion known{/CoreDistVersion get}{0}ifelse dup braindeaddistill le{(WARNING: switching to old pdfm because version =) print ==/pdfmold}{pop/pdfmnew}ifelse load}{/pdfmark where{pop{dup type /stringtype eq{externalhandler}{2 copy mark 3 1 roll{pdfmnew} stackstopped{2 copy mark 3 1 roll{pdfmold}stackstopped{ (WARNING: pdfm disabled\012)print/pdfm{pop pop}store}{ (WARNING: new pdfm failed, switching to old pdfm\012)print/pdfm/pdfmold load store}ifelse}{/pdfm/pdfmnew load store}ifelse pop pop}ifelse}}{{ pop pop}}ifelse}ifelse bind def}ifelse end def %%EndProcSet TeXDict begin 40258431 52099146 1000 600 600 (paper.dvi) @start %DVIPSBitmapFont: Fa cmbx9 9 13 /Fa 13 67 df<B512FCA816087F931D>45 D<EB03FE90383FFFE090B512F848EB07FC39 03FC01FE48486C7E4848EB7F8049133F001F15C0A2003F15E049131F007F15F0A500FF15 F8B1007F15F0A4003F15E06D133FA2001F15C0A26C6CEB7F806C6CEBFF006C6C485A3901 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[317 275 317 287] 474] def (cite.Teske) [4 [317 659 317 671] 791] def (cite.Revc97) [4 [317 582 317 594] 781] def (cite.Johnston) [4 [317 593 317 605] 791] def (cite.Oseroff) [4 [317 374 317 386] 573] def (cite.Suzuura) [4 [317 626 317 638] 791] def (cite.Ami) [4 [317 637 317 649] 791] def (figure.1) [2 [97 563 97 575] 761] def (figure.2) [3 [97 565 97 577] 763] def (figure.3) [3 [361 549 361 561] 747] def (cite.Motoyama) [4 [317 615 317 627] 791] def (cite.McRae) [4 [317 495 317 507] 693] def (cite.Zaliznyak) [4 [317 429 317 441] 627] def (cite.Zotos) [4 [317 737 317 749] 791] def (cite.Laukamp) [4 [317 396 317 408] 595] def (cite.Ren) [4 [317 308 317 320] 507] def (cite.Johnston2000) [4 [317 286 317 298] 485] def (cite.Niemeijer) [4 [317 714 317 726] 791] def (page.1) [1 [54 753 54 765] 791] def (page.2) [2 [54 753 54 765] 791] def (page.3) [3 [54 753 54 765] 791] def (page.4) [4 [54 753 54 765] 791] def (cite.Faddeev) [4 [317 560 317 572] 759] def (cite.Hase) [4 [317 363 317 375] 562] def (cite.Fujisawa) [4 [317 528 317 540] 726] def end targetdump-hook def TeXDict begin %%EndSetup %%Page: 1 1 gsave %matrix defaultmatrix setmatrix 90 rotate /stampsize 20 def /Times-Roman findfont stampsize scalefont setfont currentfont /FontBBox get aload pop /pdf@top exch 1000 div stampsize mul def pop /pdf@bottom exch 1000 div stampsize mul def pop 180 -32 moveto currentpoint /pdf@lly exch pdf@bottom add def /pdf@llx exch 2 sub def 0.5 setgray (arXiv:cond-mat/0007359v1 [cond-mat.str-el] 24 Jul 2000) show currentpoint /pdf@ury exch pdf@top add def /pdf@urx exch 2 add def /pdfmark where{pop}{userdict /pdfmark /cleartomark load put}ifelse [ /H /I /Border [0 0 1] /BS <</S/D/D[2 6]/W 1>> /Color [0 1 1] /Action << /Subtype /URI /URI (http://arxiv.org/abs/cond-mat/0007359v1)>> /Subtype /Link /Rect[pdf@llx pdf@lly pdf@urx pdf@ury] /ANN pdfmark grestore 1 0 bop 99 -97 a Fp(Thermal)37 b(conductivit)m(y)e(and)j(sp)s(eci\014c) g(heat)f(of)h(the)f(linear)g(c)m(hain)g(cuprate)h(Sr)3498 -82 y Fo(2)3537 -97 y Fp(CuO)3764 -82 y Fo(3)3804 -97 y Fp(:)910 19 y(Evidence)f(for)h(thermal)e(transp)s(ort)h(via)g (spinons)1019 231 y Fn(A.)28 b(V.)g(Sologub)r(enk)n(o,)e(E.)i(F)-7 b(elder,)27 b(K.)h(Giann\022)-42 b(o,)27 b(H.)h(R.)g(Ott)553 322 y Fm(L)l(ab)l(or)l(atorium)i(f)q(\177)-40 b(ur)27 b(F)-6 b(estk\177)-39 b(orp)l(erphysik,)31 b(ETH)d(H\177)-39 b(onggerb)l(er)l(g,)29 b(CH-8093)g(Z)q(\177)-40 b(urich,)28 b(Switzerland)1447 513 y Fn(A.)g(Vietkine,)h(A.)f(Rev)n(colevsc)n(hi) 511 605 y Fm(L)l(ab)l(or)l(atoir)l(e)i(de)e(Physic)l(o-Chimie)g(des)g (Solides,)g(Universit)n(\023)-37 b(e)28 b(Paris-Sud,)h(91405)f(Orsay,)g (F)-6 b(r)l(anc)l(e)1650 696 y Fl(\(Octob)r(er)26 b(29,)g(2018\))328 841 y(W)-6 b(e)22 b(rep)r(ort)h(measuremen)n(ts)e(of)i(the)g(sp)r (eci\014c)g(heat)f(and)h(the)f(thermal)g(conductivit)n(y)f(of)j(the)e (mo)r(del)g(Heisen)n(b)r(erg)305 933 y(spin-1/2)i(c)n(hain)f(cuprate)g (Sr)1154 941 y Fk(2)1188 933 y Fl(CuO)1346 941 y Fk(3)1404 933 y Fl(at)g(lo)n(w)h(temp)r(eratures.)33 b(In)22 b(addition)h(to)h(a) f(nearly)g(isotropic)h(phonon)f(heat)305 1024 y(transp)r(ort,)32 b(w)n(e)f(\014nd)e(a)i(quasi)f(one-dimensional)h(excess)f(thermal)g (conductivit)n(y)f(along)j(the)e(c)n(hain)g(direction,)305 1115 y(most)25 b(lik)n(ely)h(asso)r(ciated)i(with)e(spin)f(excitations) i(\(spinons\).)34 b(The)26 b(spinon)g(energy)f(curren)n(t)g(is)h (limited)g(mainly)305 1207 y(b)n(y)31 b(scattering)i(on)e(defects)i (and)e(phonons.)52 b(Analyzing)32 b(the)f(sp)r(eci\014c)h(heat)g(data,) i(the)d(in)n(trac)n(hain)h(magnetic)305 1298 y(exc)n(hange)26 b Fj(J)s(=k)757 1306 y Fi(B)836 1298 y Fl(is)g(estimated)f(to)h(b)r(e)g Fh(')p Fl(2650)h(K.)305 1464 y(P)-6 b(A)n(CS)25 b(n)n(um)n(b)r(ers:)33 b(66.70.+f,)c(75.40.Gb,)f(74.72.Jt)-67 1732 y Fn(There)47 b(is)g(a)g(considerable)e(theoretical)i(in)n(terest)g(in)g(one-)-150 1827 y(dimensional)37 b(\(1D\))h(Heisen)n(b)r(erg)f(spin-1/2)f(systems) h(b)r(ecause)-150 1923 y(they)44 b(exhibit)g(a)f(n)n(um)n(b)r(er)h(of)f (prop)r(erties)g(that)h(are)f(en)n(tirely)-150 2018 y(dominated)f(b)n (y)h(quan)n(tum-mec)n(hanical)e(b)r(eha)n(vior)g(and)i(ha)n(v)n(e)-150 2114 y(no)d(analogues)d(in)k(three-dimensional)d(systems.)73 b(In)40 b(partic-)-150 2209 y(ular,)54 b(it)c(has)f(b)r(een)g(sho)n(wn) g(that)g(the)h(Heisen)n(b)r(erg)f Fg(S)5 b Fn(=1/2)-150 2305 y(c)n(hain)38 b(represen)n(ts)e(an)i(in)n(tegrable)f(system)h(c)n (haracterized)e(b)n(y)-150 2400 y(a)41 b(macroscopic)d(n)n(um)n(b)r(er) j(of)g(conserv)-5 b(ation)39 b(la)n(ws.)1506 2370 y Ff(1)p (#cite.Zotos) [[253 433 257 445] [1 1 1 [3 3]] [0 0 1]] pdfm 1584 2400 a Fn(One)h(im-)-150 2496 y(p)r(ortan)n(t)30 b(conserv)n(ed)e(quan)n(tit)n(y)i(is)g(the)g(energy)f(curren)n(t,)1653 2465 y Ff(1)p (#cite.Zotos) [[270 421 274 433] [1 1 1 [3 3]] [0 0 1]] pdfm -1 w Fe(;)p Ff(2)p (#cite.Niemeijer) [[277 421 281 433] [1 1 1 [3 3]] [0 0 1]] pdfm 1772 2496 a Fn(im-)-150 2591 y(plying)g(an)f(ideal)g(\(in\014nite\))j (thermal)d(conductivit)n(y)g(along)g(the)-150 2686 y(c)n(hains)41 b(at)g(nonzero)f(temp)r(eratures,)k(if)e(p)r(erturbations)f(from)-150 2782 y(impurities,)26 b(phonons,)f(or)g(an)g(in)n(terc)n(hain)f (coupling,)i(whic)n(h)f(al-)-150 2877 y(w)n(a)n(ys)k(lead)h(to)g (non-in)n(tegrable)f(mo)r(dels,)i(are)f(negligible.)45 b(It)31 b(is)-150 2973 y(an)38 b(op)r(en)g(question,)j(to)d(what)h (exten)n(t)f(a)g(real)g(material)f(ma)n(y)-150 3068 y(b)r(e)43 b(regarded)d(as)i(an)g(ideal)g(in)n(tegrable)e(system.)81 b(Probably)-7 b(,)-150 3164 y(the)34 b(most)g(ob)n(vious)e(evidence)i (for)f(the)h(predicted)g(anomalous)-150 3259 y(heat)c(transp)r(ort)f (is)h(the)g(recen)n(t)g(observ)-5 b(ation)28 b(of)i(an)g(un)n(usually) -150 3355 y(high)24 b(quasi-1D)f(magnon)g(thermal)h(conductivit)n(y)g (in)g(the)g(series)-150 3450 y(\(Sr,Ca,La\))235 3462 y Ff(14)305 3450 y Fn(Cu)411 3462 y Ff(24)481 3450 y Fn(O)546 3462 y Ff(41)616 3450 y Fn(.)639 3420 y Ff(3)p (#cite.Sologubenko) [[149 307 153 319] [1 1 1 [3 3]] [0 0 1]] pdfm Fe(;)p Ff(4)p (#cite.Kudo) [[155 307 159 319] [1 1 1 [3 3]] [0 0 1]] pdfm 750 3450 a Fn(The)e(structure)f(of)g(these)h(materials)-150 3546 y(con)n(tains)29 b(t)n(w)n(o)g(building)h(blo)r(c)n(ks)g(with)g (1D)g(c)n(haracter,)f(namely)-150 3641 y(CuO)21 3653 y Ff(2)80 3641 y Fn(c)n(hains)21 b(and)h(Cu)588 3653 y Ff(2)626 3641 y Fn(O)691 3653 y Ff(3)750 3641 y Fn(ladders,)g(b)r (oth)h(orien)n(ted)e(along)g(the)-150 3737 y(same)34 b(direction.)59 b(Unfortunately)-7 b(,)36 b(the)g(dimerisation)e (within)-150 3832 y(the)c(c)n(hains)e(and)h(a)g(non-negligible)f(in)n (terc)n(hain)h(in)n(teraction)f(in)-150 3928 y(this)j(system)f (complicate)g(the)h(analysis)e(of)i(the)g(observ)n(ed)e(fea-)-150 4023 y(tures)e(in)h(terms)f(of)h(an)f(in)n(tegrable)g(mo)r(del.)-67 4119 y(In)38 b(this)g(w)n(ork,)i(w)n(e)d(ha)n(v)n(e)g(searc)n(hed)g (for)g(anomalies)g(in)h(the)-150 4214 y(thermal)43 b(transp)r(ort)f(of) h(Sr)747 4226 y Ff(2)783 4214 y Fn(CuO)954 4226 y Ff(3)991 4214 y Fn(,)k(whic)n(h)c(is)g(often)g(consid-)-150 4310 y(ered)36 b(as)g(the)g(b)r(est)h(ph)n(ysical)e(realization)g(of)i(the)f (1D)h(Heisen-)-150 4405 y(b)r(erg)g Fg(S)5 b Fn(=1/2)35 b(mo)r(del.)67 b(The)37 b(crystal)f(structure)h(of)h(Sr)1648 4417 y Ff(2)1684 4405 y Fn(CuO)1855 4417 y Ff(3)-150 4500 y Fn(con)n(tains)26 b(c)n(hains)h(formed)g(b)n(y)g(CuO)992 4512 y Ff(4)1056 4500 y Fn(squares)f(sharing)g(o)n(xygen)-150 4596 y(corners.)134 4566 y Ff(5)p (#cite.Teske) [[88 169 92 181] [1 1 1 [3 3]] [0 0 1]] pdfm 189 4596 a Fn(The)20 b(c)n(hains)f(run)h(along)f(the)h Fg(b)g Fn(axis)f(and,)i(as)e(sho)n(wn)g(in)-150 4691 y(the)28 b(inset)f(of)h(Fig.)f(2)p (#figure.2) [[127 154 132 166] [1 1 1 [3 3]] [0 0 1]] pdfm (,)g(the)h (CuO)861 4703 y Ff(4)925 4691 y Fn(squares)e(lie)h(in)h(the)g Fg(ab)f Fn(plane.)-150 4787 y(The)37 b(in)n(trac)n(hain)e(exc)n(hange)g (in)n(teraction)g(b)r(et)n(w)n(een)i(neigh)n(b)r(or-)-150 4882 y(ing)27 b(Cu)94 4852 y Ff(2+)209 4882 y Fn(ions)g(connected)g (via)g(180)1029 4852 y Fd(\016)1092 4882 y Fn(Cu-O-Cu)g(b)r(onds,)g (mea-)-150 4978 y(sured)22 b(as)h Fg(J)s(=k)299 4990 y Fe(B)356 4978 y Fn(,)h(is)f(b)r(et)n(w)n(een)g(2150)e(and)i(3000)e (K.)1421 4948 y Ff(6)p (#cite.Ami) [[243 123 246 135] [1 1 1 [3 3]] [0 0 1]] pdfm Fn({)o Ff(9)p (#cite.Johnston) [[251 123 255 135] [1 1 1 [3 3]] [0 0 1]] pdfm (#cite.Johnston) [[251 123 255 135] [1 1 1 [3 3]] [0 0 1]] pdfm 1555 4978 a Fn(The)i(ratio)-150 5073 y Fg(k)-107 5085 y Fe(B)-50 5073 y Fg(T)-1 5085 y Fe(N)62 5073 y Fg(=J)8 b Fn(,)41 b(where)d Fg(T)522 5085 y Fe(N)623 5073 y Fn(is)h(the)g(3D)g (N)n(\023)-39 b(eel)37 b(temp)r(erature,)42 b(is)c(as)-150 5169 y(small)i(as)g(2)27 b Fc(\002)f Fn(10)439 5139 y Fd(\000)p Ff(3)527 5169 y Fn(,)44 b(re\015ecting)c(an)g(extremely)g (small)g(ratio)-150 5264 y Fg(J)-96 5234 y Fd(0)-73 5264 y Fg(=J)8 b Fn(,)28 b Fg(J)128 5234 y Fd(0)179 5264 y Fn(represen)n(ting)e(the)i(in)n(terc)n(hain)e(in)n(teraction.)2125 1732 y(Our)18 b(observ)-5 b(ations)17 b(indicate)i(an)g(excess)f (thermal)h(conductiv-)2042 1827 y(it)n(y)29 b(along)f(the)h(c)n(hain)g (direction,)g(pro)n(vided)f(b)n(y)h(quasi-1D)f(spin)2042 1923 y(excitation)20 b(\(spinons\).)35 b(According)20 b(to)g(our)g(analysis)g(presen)n(ted)2042 2018 y(b)r(elo)n(w,)32 b(its)f(magnitude)h(is)f(limited)h(b)n(y)f(scattering)f(of)i(spinons) 2042 2114 y(on)18 b(defects)i(and)f(phonons.)33 b(W)-7 b(e)19 b(\014nd)h(no)e(evidence)h(for)g(a)f(m)n(utual)2042 2209 y(scattering)j(b)r(et)n(w)n(een)i(spin)f(excitations)g(and)h (hence)f(it)h(seems)f(to)2042 2305 y(b)r(e)27 b(absen)n(t)g(or)g(at)g (least)g(negligibly)f(small,)h(in)h(agreemen)n(t)e(with)2042 2400 y(theoretical)h(predictions)g(for)g(in)n(tegrable)f(mo)r(dels.) 2125 2496 y(The)46 b(sp)r(ecimens)g(used)f(in)i(these)e(exp)r(erimen)n (ts)h(w)n(ere)f(cut)2042 2591 y(from)33 b(a)g(single)f(crystal)h(that)g (had)g(b)r(een)h(gro)n(wn)e(b)n(y)h(the)h(tra)n(v-)2042 2686 y(eling)d(solv)n(en)n(t)f(\015oating)h(zone)g(metho)r(d.)49 b(The)32 b(details)f(of)g(crys-)2042 2782 y(tal)e(gro)n(wth)e(and)i (structural)f(c)n(haracterization)e(are)i(describ)r(ed)2042 2877 y(elsewhere.)2408 2847 y Ff(10)p (#cite.Revc97) [[361 375 369 387] [1 1 1 [3 3]] [0 0 1]] pdfm (#cite.Revc97) [[369 375 369 387] [1 1 1 [3 3]] [0 0 1]] pdfm 2506 2877 a Fn(F)-7 b(or)29 b(thermal)f(transp)r(ort)g(measuremen)n (ts,)g(three)2042 2973 y(rectangular-bar-shap)r(ed)49 b(samples)k(of)g(t)n(ypical)g(dimensions)2042 3068 y(2)p Fg(:)p Fn(5)9 b Fc(\002)g Fn(1)g Fc(\002)g Fn(1)22 b(mm)2559 3038 y Ff(3)2620 3068 y Fn(with)i(the)f(longest)g(dimension)g(parallel) e(to)i(ei-)2042 3164 y(ther)c(the)g Fg(a)p Fn(,)h Fg(b)f Fn(or)f Fg(c)h Fn(axis)f(w)n(ere)g(prepared.)33 b(Tw)n(o)18 b(additional)g(sam-)2042 3259 y(ples,)27 b(#1)f(and)g(#2,)h(cut)g(from) f(the)i(same)e(piece,)g(w)n(ere)g(used)h(for)2042 3355 y(sp)r(eci\014c)37 b(heat)h(measuremen)n(ts.)65 b(The)37 b(thermal)g(conductivit)n(y)2042 3450 y(w)n(as)28 b(measured)g(using)g (a)h(con)n(v)n(en)n(tional)e(steady-state)h(metho)r(d)2042 3546 y(as)i(describ)r(ed)g(in)g(Ref.)h(3)p (#cite.Sologubenko) [[407 291 412 303] [1 1 1 [3 3]] [0 0 1]] pdfm (.) 45 b(A)31 b(standard)e(relaxation)g(tec)n(hnique)2042 3641 y(w)n(as)k(emplo)n(y)n(ed)g(for)h(the)g(sp)r(eci\014c)h(heat)f (measuremen)n(ts.)55 b(The)2042 3737 y(magnetic)27 b(susceptibilit)n(y) h Fg(\037)g Fn(w)n(as)f(measured)g(with)i(a)e(commer-)2042 3832 y(cial)g(SQUID-magnetometer.)2125 3928 y(Small)50 b(amoun)n(ts)g(of)h(excess)f(o)n(xygen)f(are)g(kno)n(wn)h(to)h(b)r(e) 2042 4023 y(presen)n(t)34 b(in)i(as-gro)n(wn)c(crystals)i(of)h(Sr)3291 4035 y Ff(2)3328 4023 y Fn(CuO)3499 4035 y Ff(3)3536 4023 y Fn(,)i(giving)d(rise)g(to)2042 4119 y(a)40 b(Curie-W)-7 b(eiss)40 b(term)h(in)g(the)g(temp)r(erature)f(dep)r(endence)h(of)2042 4214 y(the)36 b(magnetic)g(susceptibilit)n(y)3033 4184 y Ff(6)p (#cite.Ami) [[436 215 440 227] [1 1 1 [3 3]] [0 0 1]] pdfm 3106 4214 a Fn(due)g(to)g(uncomp)r(ensated)g(Cu)2042 4310 y Fg(S)5 b Fn(=1/2)32 b(spins.)57 b(In)35 b(order)e(to)h(study)g (the)h(in\015uence)g(of)f(excess)2042 4405 y(o)n(xygen,)25 b(w)n(e)g(annealed)h(sample)g(#2)f(at)h(870)3446 4375 y Fd(\016)3483 4405 y Fn(C)g(for)g(72)f(h)h(under)2042 4500 y(argon)k(atmosphere,)h(as)g(describ)r(ed)g(in)h(Ref.)g(8)p (#cite.Motoyama) [[492 177 498 189] [1 1 1 [3 3]] [0 0 1]] pdfm (.)49 b(F)-7 b(rom)31 b(the)h(re-)2042 4596 y(sults)25 b(of)h(our)e (measuremen)n(ts)h(of)g Fg(\037)p Fn(\()p Fg(T)12 b Fn(\),)26 b(the)g(ratio)e(of)h(the)h(n)n(um-)2042 4691 y(b)r(er)34 b(of)g(residual)g(spin-1/2)f(impurities)h(to)h(the)f(total)g(n)n(um)n (b)r(er)2042 4787 y(of)e(Cu)g(ions)f(w)n(as)g(estimated)h(to)f(b)r(e)h (1.8)p Fc(\002)p Fn(10)3479 4757 y Fd(\000)p Ff(4)3598 4787 y Fn(for)f(the)i(unan-)2042 4882 y(nealed)f(sample)f(#1)h(and)g(6) p Fc(\002)p Fn(10)3086 4852 y Fd(\000)p Ff(5)3205 4882 y Fn(for)g(the)g(annealed)g(sample)2042 4978 y(#2.)2125 5073 y(The)d(results)h(of)f(the)h(sp)r(eci\014c)g(heat)f(\()p Fg(C)3373 5085 y Fe(p)3412 5073 y Fn(\))h(measuremen)n(ts)f(in)2042 5169 y(the)39 b(temp)r(erature)f(range)f(b)r(et)n(w)n(een)i(1.5)f(and)g (22)g(K)g(are)g(pre-)2042 5264 y(sen)n(ted)30 b(in)h(Fig.)g(1)p (#figure.1) [[381 85 386 97] [1 1 1 [3 3]] [0 0 1]] pdfm 30 w(as)f(a)g(plot)h(of)f Fg(C)3153 5276 y Fe(p)3192 5264 y Fg(=T)41 b Fn(v)n(ersus)30 b Fg(T)3639 5234 y Ff(2)3675 5264 y Fn(.)46 b(The)31 b(solid)1946 5608 y(1)p eop %%Page: 2 2 2 1 bop -48 1214 a @beginspecial 83 @llx 47 @lly 864 @urx 598 @ury 2205 @rwi @setspecial %%BeginDocument: Cp.eps /proFitdict 44 dict def proFitdict begin /Pbd {bind def}def /Pm {moveto} def /Prm {rmoveto} def /Pl {lineto} def /Ps {gsave} def /Pr {grestore} def /Pt {stroke} def /Pw {setlinewidth} def /Pc {setrgbcolor} def /Pg {setgray} def /Pfb {newpath dup 5 -1 roll Pm 3 1 roll dup 3 -1 roll Pl Px Pl Px Pl fill}Pbd /Pfr {newpath 4 -1 roll dup 5 1 roll Pm 2 1 roll dup 3 1 roll Pl Px 2 1 roll Pl Px 2 1 roll Pl fill}Pbd /Po0 {3 -1 roll exch 2 mul add 3 div 3 1 roll 2 mul 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b(for)g(the)g(temp)r(er-)-150 2544 y(ature)d(region)g(near)g (and)g(b)r(elo)n(w)h Fg(T)988 2556 y Ff(max)1114 2544 y Fn(,)i(where)d(the)h(in\015uence)-150 2640 y(of)j(sample)f(b)r (oundaries)g(and)h(v)-5 b(arious)38 b(defects)h(is)g(imp)r(ortan)n(t) -150 2735 y(and,)33 b(therefore,)g(the)f(b)r(eha)n(vior)f(of)h Fg(\024)p Fn(\()p Fg(T)12 b Fn(\))32 b(is,)h(to)f(some)f(exten)n(t,) -150 2831 y(sample-dep)r(enden)n(t.)75 b(Our)40 b(\014tting)g(of)h Fg(\024)1200 2843 y Fe(c)1233 2831 y Fn(\()p Fg(T)12 b Fn(\))40 b(and)g Fg(\024)1620 2843 y Fe(a)1660 2831 y Fn(\()p Fg(T)12 b Fn(\))40 b(of)-150 2926 y(Sr)-71 2938 y Ff(2)-34 2926 y Fn(CuO)137 2938 y Ff(3)174 2926 y Fn(,)f(emplo)n(ying)d(the)h(Deb)n(y)n(e)f(mo)r(del)h(of)g(phonon)f (ther-)-150 3022 y(mal)27 b(conductivit)n(y)f(in)h(a)f(similar)g(w)n(a) n(y)g(as)g(describ)r(ed)h(in)g(Ref.)g(3)p (#cite.Sologubenko) [[291 354 296 366] [1 1 1 [3 3]] [0 0 1]] pdfm (,) -150 3117 y(has)k(sho)n(wn)g(that)i(the)f(in\015uence)g(of)g(b)r (oundary)f(scattering)g(on)-150 3213 y(the)f(thermal)f(conductivit)n(y) g(is)g(negligible)f(at)i Fg(T)37 b Fc(\025)25 b Fn(50)j(K.)h(The)-150 3308 y(same)21 b(calculation)h(indicates)g(that)g(an)g(enhanced)f (phonon)h(con-)-150 3404 y(tribution)i(to)g Fg(\024)343 3416 y Fe(b)400 3404 y Fn(b)r(elo)n(w)f(50)g(K)h(ma)n(y)f(mostly)g(b)r (e)h(traced)g(bac)n(k)f(to)-150 3499 y(an)28 b(enhanced)f(phonon)h (mean)g(free)f(path)h(whic)n(h)g(is)g(limited)h(b)n(y)-150 3595 y(b)r(oundary)23 b(and)h(defect)g(scattering.)35 b(Based)23 b(on)g(all)h(these)g(argu-)-150 3690 y(men)n(ts)29 b(presen)n(ted)f(ab)r(o)n(v)n(e,)g(w)n(e)g(mak)n(e)g(the)h(crucial)f (assumption)-150 3786 y(that)37 b(the)h(phonon)e(thermal)h(conductivit) n(y)g(at)g Fg(T)49 b Fc(\025)39 b Fn(50)d(K)h(is)-150 3881 y(almost)27 b(isotropic.)-67 3977 y(In)34 b(order)f(to)g (single-out)g(the)i(heat)e(transp)r(ort)g(due)i(to)e(spin)-150 4072 y(excitations,)k(the)f(phonon)f(thermal)h(conductivit)n(y)-7 b(,)37 b(a)n(v)n(eraged)-150 4167 y(o)n(v)n(er)23 b(the)j Fg(a)p Fn(-)e(and)h Fg(c)p Fn(-directions)f(at)h Fg(T)34 b Fc(\025)23 b Fn(50)h(K,)h(w)n(as)f(subtracted)-150 4263 y(from)39 b(the)i(exp)r(erimen)n(tal)e(data)g(of)h Fg(\024)1078 4275 y Fe(b)1111 4263 y Fn(.)73 b(The)40 b(resulting)f(spin)-150 4358 y(part)34 b Fg(\024)85 4370 y Fe(s)155 4358 y Fn(is)h(also)f(plotted)h(in)g(Fig.)f(2)p (#figure.2) [[191 194 196 206] [1 1 1 [3 3]] [0 0 1]] pdfm (.)58 b(In)35 b(a)f(\014rst)h(appro)n(xima-)-150 4454 y(tion,)28 b(v)-5 b(alid)27 b(for)g(an)n(y)g(system)h(of)f(quasiparticles,)f(the)i (1D)g(ther-)-150 4549 y(mal)20 b(conductivit)n(y)h(is)f(giv)n(en)g(b)n (y)g(the)h(simple)g(kinetic)g(expression)-150 4645 y Fg(\024)-102 4657 y Fe(s)-44 4645 y Fn(=)i Fg(C)103 4657 y Fe(s)139 4645 y Fg(v)179 4657 y Fe(s)215 4645 y Fg(l)240 4657 y Fe(s)299 4645 y Fn(where)g Fg(C)594 4657 y Fe(s)654 4645 y Fn(is)h(the)h(sp)r(eci\014c)f(heat,)g Fg(v)1403 4657 y Fe(s)1463 4645 y Fn(is)g(the)g(v)n(elo)r(c-)-150 4740 y(it)n(y)-7 b(,)30 b(and)g Fg(l)182 4752 y Fe(s)247 4740 y Fn(is)g(the)g(mean)g(free)f(path)h(of)g(the)g(spin)g (excitations.)-150 4836 y(The)39 b(v)n(elo)r(cit)n(y)g(of)g(spinons)g (is)821 4806 y Ff(11)p (#cite.Faddeev) [[171 140 178 152] [1 1 1 [3 3]] [0 0 1]] pdfm (#cite.Faddeev) [[178 140 178 152] [1 1 1 [3 3]] [0 0 1]] pdfm 931 4836 a Fg(v)971 4848 y Fe(s)1049 4836 y Fn(=)k Fg(J)8 b(a\031)s(=)p Fn(2\026)-42 b Fg(h)o Fn(,)42 b(where)d Fg(a)h Fn(is)-150 4931 y(the)25 b(distance)g(b)r(et)n(w)n(een)g(the)g (spins)g(along)f(the)h(c)n(hain)g(direction.)-150 5027 y(Since)k Fg(T)36 b Fc(\034)25 b Fg(J)s(=k)395 5039 y Fe(B)481 5027 y Fn(still)k(holds,)g(Eq.)f(\(2)p (#equation.2) [[200 114 205 126] [1 1 1 [3 3]] [0 0 1]] pdfm (\))h (for)f(the)i(sp)r(eci\014c)f(heat)-150 5122 y(is)g(v)-5 b(alid,)30 b(and)f(th)n(us)g(the)h(thermal)f(conductivit)n(y)g(of)g (spinons)g(is)-150 5218 y(giv)n(en)e(b)n(y)g(the)h(simple)g(equation) 2144 1344 y @beginspecial 98 @llx 41 @lly 778 @urx 569 @ury 2205 @rwi @setspecial 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241] [1 1 1 [3 3]] [0 0 1]] pdfm (\))g(is) h(to)f(represen)n(t)f(Umklapp)2042 4161 y(pro)r(cesses,)24 b(spinon-spinon)g(scattering)h(ma)n(y)f(b)r(e)i(ruled)f(out)g(b)r(e-) 2042 4256 y(cause)36 b(this)h(case)e(w)n(ould)h(require)g Fg(T)3229 4226 y Fd(\003)3303 4256 y Fn(to)g(b)r(e)h(of)g(the)g(order)e (of)2042 4352 y Fg(J)s(=k)2176 4364 y Fe(B)2256 4352 y Fc(\030)p Fn(2600)17 b(K.)i(Since)g Fg(T)2882 4322 y Fd(\003)2939 4352 y Fn(is)g(close)f(to)i(\002)3363 4364 y Fe(D)3422 4352 y Fg(=)p Fn(2=220)d(K,)i(spinon-)2042 4447 y(phonon)24 b(Umklapp)h(pro)r(cesses)f(are)f(the)j(most)e(lik)n (ely)h(c)n(hoice)f(for)2042 4543 y(this)k(con)n(tribution.)2125 4638 y(The)f(second)f(and)g(constan)n(t)g(term)h(in)f(Eq.)h(\(4)p (#equation.4) [[496 160 501 172] [1 1 1 [3 3]] [0 0 1]] pdfm (\))f(is) h(attributed)2042 4734 y(to)33 b(scattering)g(of)h(spin)f(excitations)g (on)h(defects)g(in)n(terrupting)2042 4829 y(the)g(Cu-O)f(c)n(hains.)56 b(In)34 b(that)g(case)f(the)i(v)-5 b(alue)33 b(of)h(the)h(param-)2042 4925 y(eter)f Fg(L)f Fn(is)h(a)g(measure)f(for)h(the)g(mean)g(distance) g(b)r(et)n(w)n(een)g(the)2042 5020 y(defects.)42 b(Surprisingly)-7 b(,)29 b(this)h(distance)f(is)g(m)n(uc)n(h)g(shorter)f(than)2042 5116 y(the)k(a)n(v)n(erage)d(distance)j(of)g(2)p Fc(\002)p Fn(10)3109 5085 y Ff(4)3176 5101 y Fn(\027)3176 5116 y(A)g(b)r(et)n(w)n(een)g Fg(S)5 b Fn(=1/2)30 b(impu-)2042 5211 y(rities,)k(estimated)f(from)g(the)h(Curie-W)-7 b(eiss-t)n(yp)r(e)32 b(term)h(of)g(the)2042 5307 y(magnetic)h (susceptibilit)n(y)-7 b(.)59 b(A)35 b(similar)f(discrepancy)g(has)g (also)1946 5608 y(3)p eop %%Page: 4 4 4 3 bop -150 -83 a Fn(b)r(een)24 b(encoun)n(tered)e(in)h(the)h(in)n (terpretation)e(of)h(NMR)h(measure-)-150 12 y(men)n(ts)j(on)g(Sr)286 24 y Ff(2)323 12 y Fn(CuO)494 24 y Ff(3)531 12 y Fn(.)554 -18 y Ff(27)p (#cite.Takigawa97_55) [[138 719 146 731] [1 1 1 [3 3]] [0 0 1]] pdfm (#cite.Takigawa97_55) [[146 719 146 731] [1 1 1 [3 3]] [0 0 1]] pdfm 652 12 a Fn(Recen)n(tly)-7 b(,)27 b(in)g(order)f(to)h(explain)g(some) -150 108 y(p)r(eculiar)32 b(features)h(of)f(NMR)i(sp)r(ectra)e(of)h(Sr) 1294 120 y Ff(2)1331 108 y Fn(CuO)1502 120 y Ff(3)1539 108 y Fn(,)h(Bouc)n(her)-150 203 y(and)22 b(T)-7 b(akiga)n(w)n(a)350 173 y Ff(32)p (#cite.Boucher) [[114 696 122 708] [1 1 1 [3 3]] [0 0 1]] pdfm (#cite.Boucher) [[122 696 122 708] [1 1 1 [3 3]] [0 0 1]] pdfm 441 203 a Fn(in)n(tro)r(duced)22 b(the)h(concept)g(of)f(mobile)h(\\b)r (ond-)-150 299 y(defects",)k(whic)n(h)g(are)f(not)g(related)h(to)f(in)n (terstitial)h(excess)f(o)n(xy-)-150 394 y(gen.)54 b(The)33 b(calculated)g(mean)g(distance)g(b)r(et)n(w)n(een)g(t)n(w)n(o)g(neigh-) -150 490 y(b)r(oring)d(b)r(ond-defects,)j(consisten)n(t)d(with)i(the)g (NMR)g(data)e(b)r(e-)-150 585 y(t)n(w)n(een)39 b(20)g(and)g(60)g(K,)604 555 y Ff(32)p (#cite.Boucher) [[144 650 152 662] [1 1 1 [3 3]] [0 0 1]] pdfm (#cite.Boucher) [[152 650 152 662] [1 1 1 [3 3]] [0 0 1]] pdfm 713 585 a Fn(is)h(sho)n(wn)e(in)i(Fig.)f(3)p (#figure.3) [[235 647 240 659] [1 1 1 [3 3]] [0 0 1]] pdfm (.)73 b(W)-7 b(e)39 b(note)h(a)-150 681 y(reasonably)21 b(go)r(o)r(d)i(o)n(v) n(erlap)e(with)j(our)f(data)g(of)g Fg(l)1371 693 y Fe(s)1430 681 y Fn(at)g Fg(T)35 b Fn(=)22 b(60)h(K.)-150 776 y(The)41 b(mo)r(del)g(of)g(Bouc)n(her)f(and)h(T)-7 b(akiga)n(w)n(a)38 b(predicts)j(that)h(at)-150 872 y(lo)n(w)n(er)20 b(temp)r(eratures)i (the)g(in)n(teraction)f(b)r(et)n(w)n(een)h(defects)g(is)f(im-)-150 967 y(p)r(ortan)n(t)32 b(and)g(the)h(n)n(um)n(b)r(er)f(of)h(b)r (ond-defects)f(decreases)f(with)-150 1063 y(increasing)j(temp)r (erature.)62 b(If)36 b(our)f(parameter)f Fg(L)i Fn(in)g(Eq.)f(\(4)p (#equation.4) [[290 589 295 601] [1 1 1 [3 3]] [0 0 1]] pdfm (\))-150 1158 y(indeed)f(represen)n(ts)e(the)i(distance)g(b)r(et)n(w)n(een)g(b)r (ond-defects,)h(it)-150 1254 y(ough)n(t)19 b(to)h(b)r(e)g(temp)r (erature-dep)r(enden)n(t)g(b)r(elo)n(w)f(50)g(K.)g(Unfortu-)-150 1349 y(nately)-7 b(,)28 b(a)f(quan)n(titativ)n(e)g(c)n(hec)n(k)f(of)i 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2208 y Fn(is)f(isotropic)g(also)f(in)i (this)g(temp)r(era-)-150 2304 y(ture)21 b(range)e(and)h(equal)h(to)f (the)h(a)n(v)n(erage)d(of)j Fg(\024)1262 2316 y Fe(c)1316 2304 y Fn(and)f Fg(\024)1518 2316 y Fe(a)1579 2304 y Fn(and,)i(sec-)-150 2399 y(ond)27 b(that)h Fg(l)216 2411 y Fe(s)278 2399 y Fn(is)g(equal)e(to)i(the)f(distance)g(b)r(et)n(w)n (een)h(neigh)n(b)r(oring)-150 2495 y(b)r(ond-defects)e(giv)n(en)g(in)g (Ref.)h(32)p (#cite.Boucher) [[170 418 180 430] [1 1 1 [3 3]] [0 0 1]] pdfm 26 w(\(the)f(dashed)g(line)h(in)f(Fig.)g(3)p (#figure.3) [[287 418 292 430] [1 1 1 [3 3]] [0 0 1]] pdfm (\).)-150 2590 y(The)37 b(resulting)g(temp)r(erature)g(dep)r(endence)h(of)f Fg(\024)1472 2602 y Fe(b)1543 2590 y Fn(sho)n(wn)g(b)n(y)-150 2686 y(the)d(solid)f(line)h(in)f(Fig.)h(2)p (#figure.2) [[149 395 154 407] [1 1 1 [3 3]] [0 0 1]] pdfm 33 w(is)f(in)h(qualitativ)n(e)f(agreemen)n(t)f(with)-150 2781 y(the)c(exp)r(erimen)n(t.)420 2751 y Ff(33)p (#cite.Comment1) [[122 387 130 399] [1 1 1 [3 3]] [0 0 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y(mal)19 b(conductivit)n(y)-7 b(,)20 b(in)f(agreemen)n(t)f(with)h(the)g(predictions)g(made)-150 3831 y(for)27 b(in)n(tegrable)f(mo)r(dels.)637 3801 y Ff(1)p (#cite.Zotos) [[148 261 152 273] [1 1 1 [3 3]] [0 0 1]] pdfm 702 3831 a Fn(Our)h(results)g(imply)h(that)g(a)f(dissipa-)-150 3927 y(tionless)j(energy)f(curren)n(t,)i(exp)r(ected)g(for)f(systems)g (that)h(ful\014ll)-150 4022 y(the)e(assumptions)e(of)h(the)h(in)n (tegrable)e(Heisen)n(b)r(erg)g(1D)i Fg(S)5 b Fn(=1/2)-150 4118 y(mo)r(del,)25 b(is)g(not)f(robust)g(if)i(p)r(erturbations)d(lik)n (e)i(defects)f(and)h(lat-)-150 4213 y(tice)20 b(excitations)g(in)n (terfere.)34 b(The)20 b(v)n(ery)f(high)h(v)-5 b(alue)20 b(of)g(the)g(mag-)-150 4309 y(netic)26 b(exc)n(hange)f(in)n(teraction)g (within)h(the)h(c)n(hains)e(and)h(the)g(lo)n(w)-150 4404 y(temp)r(erature)21 b(magnetic)f(phase)h(transition,)h(iden)n(ti\014ed) g(via)e(our)-150 4500 y(sp)r(eci\014c)29 b(heat)g(measuremen)n(ts,)f (con\014rm)g(that)h(Sr)1450 4512 y Ff(2)1487 4500 y Fn(CuO)1658 4512 y Ff(3)1724 4500 y Fn(ma)n(y)-7 b(,)-150 4595 y(nev)n(ertheless,) 27 b(b)r(e)i(considered)f(as)f(an)h(excellen)n(t)h(realization)d(of) -150 4691 y(a)h(1D)h Fg(S)5 b Fn(=1/2)25 b(Heisen)n(b)r(erg)i(an)n (tiferromagnet.)-67 4786 y(W)-7 b(e)30 b(ac)n(kno)n(wledge)e(useful)j (discussions)e(with)h(X.)h(Zotos)e(and)-150 4882 y(F.)40 b(Naef.)73 b(This)40 b(w)n(ork)e(w)n(as)h(\014nancially)g(supp)r(orted) g(in)h(part)-150 4977 y(b)n(y)34 b(the)h(Sc)n(h)n(w)n(eizerisc)n(he)d (Nationalfonds)h(zur)h(F\177)-42 b(orderung)33 b(der)-150 5073 y(Wissensc)n(haftlic)n(hen)27 b(F)-7 b(orsc)n(h)n(ung.)p -150 5291 2043 4 v 2078 -115 a Fk(1)2129 -83 y Fl(X.)17 b(Zotos,)k(F.)d(Naef,)i(and)d(P)-6 b(.)18 b(Prelo)n(v)l(\024)-34 b(sek,)20 b(Ph)n(ys.)d(Rev.)g(B)h Fa(55)p Fl(,)i(11029)2129 8 y(\(1997\).)2078 68 y Fk(2)2129 100 y Fl(Th.)k(Niemeijer)f(and)g(H.)g (A.)h(W.)f(v)l(an)g(Vianen,)h(Ph)n(ys.)f(Lett.)h Fa(34A)p Fl(,)2129 191 y(401)j(\(1971\).)2078 251 y Fk(3)2129 282 y Fl(A.)h(V.)h(Sologub)r(enk)n(o,)h(K.)e(Giann\022)-38 b(o,)31 b(H.)d(R.)h(Ott,)g(U.)g(Ammerahl,)2129 374 y(and)c(A.)h(Rev)n (colevsc)n(hi,)f(Ph)n(ys.)h(Rev.)f(Lett.)h Fa(84)p Fl(,)g(2714)h (\(2000\).)2078 433 y Fk(4)2129 465 y Fl(K.)e(Kudo)g Fm(et)k(al.)p Fl(,)c(J.)h(Lo)n(w)h(T)-6 b(emp.)24 b(Ph)n(ys.)i Fa(117)p Fl(,)g(1689)i(\(1999\).)2078 525 y Fk(5)2129 556 y Fl(Chr.)d(L.)g(T)-6 b(esk)n(e)24 b(and)g(Hk.)g(Muller-B)r(\177) -41 b(usc)n(h)n(baum,)25 b(Z.)g(Anorg.)g(Allg.)2129 648 y(Chem.)g Fa(371)p Fl(,)h(325)h(\(1969\).)2078 707 y Fk(6)2129 739 y Fl(T.)f(Ami)f Fm(et)j(al.)p Fl(,)d(Ph)n(ys.)h(Rev.)f(B) h Fa(51)p Fl(,)g(5994)h(\(1995\).)2078 798 y Fk(7)2129 830 y Fl(H.)e(Suzuura)g Fm(et)j(al.)p Fl(,)e(Ph)n(ys.)f(Rev.)g(Lett.)h Fa(76)p Fl(,)g(2579)i(\(1996\).)2078 890 y Fk(8)2129 922 y Fl(N.)f(Moto)n(y)n(ama,)i(H.)f(Eisaki,)i(and)e(S.)f(Uc)n(hida,)i (Ph)n(ys.)f(Rev.)f(Lett.)2129 1013 y Fa(76)p Fl(,)f(3212)h(\(1996\).) 2078 1072 y Fk(9)2129 1104 y Fl(D.)e(C.)i(Johnston,)f(Acta)g(Ph)n(ys.)f (P)n(ol.)i(A)e Fa(91)p Fl(,)h(181)h(\(1997\).)2047 1164 y Fk(10)2129 1196 y Fl(A.)d(Rev)n(colevsc)n(hi,)i(A.)e(Vietkine,)h(and) g(H.)g(Moudden,)f(Ph)n(ysica)i(C)2129 1287 y Fa(282-287)p Fl(,)h(493)g(\(1997\).)2047 1346 y Fk(11)2129 1378 y Fl(L.)e(D.)g(F)-6 b(addeev)25 b(and)f(L.)i(A.)f(T)-6 b(akh)n(ta)t(jan,)26 b(Ph)n(ys.)f(Lett.)g Fa(85A)p Fl(,)h(375)2129 1469 y(\(1981\).)2047 1529 y Fk(12)2129 1561 y Fl(O.)f(V.)h(Miso)r(c)n (hk)n(o)g Fm(et)j(al.)p Fl(,)c(Ph)n(ys.)h(Rev.)f(B)h Fa(53)p Fl(,)g(14733)i(\(1996\).)2047 1620 y Fk(13)2129 1652 y Fl(H.)d(F)-6 b(ujisa)n(w)n(a)27 b Fm(et)i(al.)p Fl(,)c(Ph)n(ys.)g(Rev.)g(B)h Fa(59)p Fl(,)h(7358)g(\(1999\).)2047 1712 y Fk(14)2129 1743 y Fl(M.)f(T)-6 b(ak)l(ahashi,)26 b(Prog.)h(Theor.)g(Ph)n(ys.)f Fa(50)p Fl(,)g(1519)h(\(1973\).)2047 1803 y Fk(15)2129 1835 y Fl(F.)f(D.)f(M.)i(Haldane,)f(Ph)n(ys.)f(Rev.)g (Lett.)h Fa(66)p Fl(,)h(1529)g(\(1991\).)2047 1894 y Fk(16)2129 1926 y Fl(W.)22 b(McRae)g(and)g(O.)g(P)-6 b(.)22 b(Sushk)n(o)n(v,)f(Ph)n(ys.)h(Rev.)f(B)i Fa(58)p Fl(,)g(62)f(\(1998\).)2047 1986 y Fk(17)2129 2017 y Fl(J.)k(Lorenzana)h (and)e(R.)g(Eder,)h(Ph)n(ys.)g(Rev.)f(B)h Fa(55)p Fl(,)g(3358)i (\(1997\).)2047 2077 y Fk(18)2129 2109 y Fl(M.)58 b(T)-6 b(akiga)n(w)n(a,)68 b(O.)58 b(A.)g(Starykh,)65 b(A.)58 b(W.)g(Sandvik,)65 b(and)2129 2200 y(R.)25 b(R.)h(P)-6 b(.)25 b(Singh,)h(Ph)n(ys.)g(Rev.)f(B)h Fa(56)p Fl(,)g(13681)i (\(1997\).)2047 2260 y Fk(19)2129 2291 y Fl(A.)d(Keren)h Fm(et)i(al.)p Fl(,)d(Ph)n(ys.)h(Rev.)f(B)h Fa(48)p Fl(,)g(12926)i (\(1993\).)2047 2351 y Fk(20)2129 2383 y Fl(K.)d(M.)i(Ko)t(jima)f Fm(et)i(al.)p Fl(,)d(Ph)n(ys.)h(Rev.)f(Lett.)h Fa(78)p Fl(,)g(1787)h(\(1997\).)2047 2442 y Fk(21)2129 2474 y Fl(I.)e(A.)h(Zalizn)n(y)n(ak)f Fm(et)k(al.)p Fl(,)c(Ph)n(ys.)g(Rev.)h (Lett.)f Fa(83)p Fl(,)i(5370)g(\(1999\).)2047 2534 y Fk(22)2129 2565 y Fl(S.)k(Eggert)i(and)e(I.)g(A\017ec)n(k,)i(Ph)n(ys.)e (Rev.)g(B)h Fa(46)p Fl(,)i(10866)f(\(1992\);)2129 2657 y(Ph)n(ys.)25 b(Rev.)g(Lett.)h Fa(75)p Fl(,)h(934)f(\(1995\).)2047 2716 y Fk(23)2129 2748 y Fl(M.)g(Lauk)l(amp)e Fm(et)k(al.)p Fl(,)d(Ph)n(ys.)h(Rev.)f(B)h Fa(57)p Fl(,)h(10755)g(\(1998\).)2047 2808 y Fk(24)2129 2839 y Fl(M.)f(Azuma)e Fm(et)29 b(al.)p Fl(,)c(Ph)n(ys.)g(Rev.)h(B)g Fa(55)p Fl(,)g(8658)h(\(1997\).)2047 2899 y Fk(25)2129 2931 y Fl(S.)e(B.)i(Osero\013)f Fm(et)i(al.)p Fl(,)d(Ph)n(ys.)h(Rev.)f(Lett.)h Fa(74)p Fl(,)g(1450)h(\(1995\).)2047 2990 y Fk(26)2129 3022 y Fl(M.)f(Hase)g Fm(et)i(al.)p Fl(,)e(Ph)n(ysica)g(\(Amsterdam\))d Fa(215B)p Fl(,)j(164)h(\(1995\).) 2047 3082 y Fk(27)2129 3113 y Fl(M.)40 b(T)-6 b(akiga)n(w)n(a,)44 b(N.)c(Moto)n(y)n(ama,)j(H.)c(Eisaki,)44 b(and)39 b(S.)g(Uc)n(hida,) 2129 3205 y(Ph)n(ys.)25 b(Rev.)g(B)h Fa(55)p Fl(,)h(14129)g(\(1997\).) 2047 3264 y Fk(28)2129 3296 y Fl(R.)39 b(Berman,)j Fm(Thermal)e (Conduction)i(in)d(Solids)p Fl(,)k(\(Clarendon,)2129 3387 y(Oxford,)25 b(1976\).)2047 3447 y Fk(29)2129 3479 y Fl(S.)g(Y.)h(Ren)f(and)g(J.)h(D.)g(Do)n(w,)g(Ph)n(ys.)g(Rev.)f(B)h Fa(25)p Fl(,)g(3750)i(\(1982\).)2047 3538 y Fk(30)2129 3570 y Fl(D.)d(L.)h(Hub)r(er,)f(Prog.)i(Theor.)g(Ph)n(ys.)f Fa(39)p Fl(,)g(1170)h(\(1968\).)2047 3630 y Fk(31)2129 3661 y Fl(D.)e(C.)i(Johnston)f Fm(et)i(al.)p Fl(,)d(Ph)n(ys.)h(Rev.)f (B)h Fa(61)p Fl(,)g(9558)h(\(2000\).)2047 3721 y Fk(32)2129 3753 y Fl(J.)38 b(P)-6 b(.)38 b(Bouc)n(her)g(and)g(M.)g(T)-6 b(akiga)n(w)n(a,)43 b(Ph)n(ys.)38 b(Rev.)f(B)h Fa(62)p Fl(,)k(367)2129 3844 y(\(2000\).)2047 3904 y Fk(33)2129 3935 y Fl(Note)29 b(that)f(the)h(p)r(ossibilit)n(y)h(of)g(an)f (enhanced)f(lo)n(w-temp)r(erature)2129 4027 y(phonon)h(mean)g(free)i (path)e(along)i(the)e Fj(b)h Fl(axis)h(is)f(not)g(tak)n(en)f(in)n(to) 2129 4118 y(accoun)n(t)c(in)h(this)g(calculation.)1946 5608 y Fn(4)p eop %%Trailer end end userdict /end-hook known{end-hook}if %%EOF