Monte Carlo Wang-Landau_antiferromagnetic perovskite

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It may not display this or other websites correctly.<br />You should upgrade or use an <a href="https://www.google.com/chrome/" target="_blank" rel="noopener">alternative browser</a>.</div> <div class="p-body-main p-body-main--withSidebar "> <div class="p-body-contentCol"></div> <div class="p-body-sidebarCol"></div> <div class="p-body-content"> <div class="p-body-pageContent"> <div class="p-breadcrumbs--parent "> <ul class="p-breadcrumbs " itemscope itemtype="https://schema.org/BreadcrumbList"> <li itemprop="itemListElement" itemscope itemtype="https://schema.org/ListItem"> <a href="https://www.physicsforums.com/" itemprop="item"> <span itemprop="name">Forums</span> </a> <meta itemprop="position" content="1" /> </li> <li itemprop="itemListElement" itemscope itemtype="https://schema.org/ListItem"> <a href="/#physics.9" itemprop="item"> <span itemprop="name">Physics</span> </a> <meta itemprop="position" content="2" /> </li> <li itemprop="itemListElement" itemscope itemtype="https://schema.org/ListItem"> <a href="/forums/atomic-and-condensed-matter.64/" itemprop="item"> <span itemprop="name">Atomic and Condensed Matter</span> </a> <meta itemprop="position" content="3" /> </li> </ul> </div> <div class="p-body-header"> <div class="p-title "> <h1 class="p-title-value"> Monte Carlo Wang-Landau_antiferromagnetic perovskite </h1> </div> <div class="p-description"> <ul class="listInline listInline--bullet"> <li> <span data-xf-init="tooltip" title="Level: Advanced (Grad)" ><span class="prefix advanced" dir="auto">A</span></span> </li> <li> <i class="fa--xf fal fa-user" aria-hidden="true" title="Thread starter"></i> <span class="u-srOnly">Thread starter</span> <span>UFSJ</span> </li> <li> <i class="fa--xf fal fa-clock" aria-hidden="true" title="Start date"></i> <span class="u-srOnly">Start date</span> <time class="u-dt" dir="auto" datetime="2023-08-28T08:02:53-0500" data-time="1693227773" data-date-string="Aug 28, 2023" data-time-string="8:02 AM" title="Aug 28, 2023 at 8:02 AM">Aug 28, 2023</time> </li> </ul> </div> </div> <div class="block-container lbContainer" style="padding:5px;"> In summary, the study on "Monte Carlo Wang-Landau antiferromagnetic perovskite" explores the application of the Wang-Landau algorithm in the context of antiferromagnetic materials, specifically perovskites. It focuses on the computational methods used to analyze the magnetic properties and phase transitions in these materials, highlighting the effectiveness of the Monte Carlo simulations in understanding complex magnetic behavior. The findings contribute to the knowledge of the thermodynamic characteristics of antiferromagnetic perovskites, which are significant for their potential applications in advanced electronic devices. </div> <script src="https://www.physicsforums.com/check-for-tex.js" defer></script> <div class="block block--messages" data-xf-init="" data-type="post" data-href="/inline-mod/" data-search-target="*"> <span class="u-anchorTarget" id="posts"></span> <div class="block-outer"></div> <div class="block-outer js-threadStatusField"></div> <div class="block-container lbContainer" data-xf-init="lightbox select-to-quote old-new-message-indicator" data-sv-live-content-time-element-selector=".message-attribution-main time.u-dt" data-message-selector=".js-post" data-lb-id="thread-1055241" data-lb-universal="0"> <div class="block-body js-replyNewMessageContainer">  <article class="message message--post js-post js-inlineModContainer " data-author="UFSJ" data-content="post-6926869" id="js-post-6926869" > <span class="u-anchorTarget" id="post-6926869"></span> <div class="message-header"> <header class="message-attribution message-attribution--split"> <ul class="message-attribution-main listInline "> <li class="u-concealed"> <time class="u-dt" dir="auto" datetime="2023-08-28T08:02:53-0500" data-time="1693227773" data-date-string="Aug 28, 2023" data-time-string="8:02 AM" title="Aug 28, 2023 at 8:02 AM">Aug 28, 2023</time> </li> </ul> <ul class="message-attribution-opposite message-attribution-opposite--list "> <li> <span style="cursor:pointer;" data-xf-init="share-tooltip" data-href="/posts/6926869/share" aria-label="Share" role="button" rel="nofollow"> <i class="fa--xf fal fa-share-alt" aria-hidden="true"></i> </span> </li> <li> #1 </li> </ul> </header> </div> <div class="message-inner"> <div class="message-cell message-cell--user"> <section class="message-user" > <div class="message-userDetails"> <span class="message-name"><span class="username " dir="auto" data-user-id="646881">UFSJ</span></span>   <span class="threadstarter" data-xf-init="tooltip" title="Thread Starter"><i class="fal fa-user-edit"></i></span>   </div> <div class="message-userExtras"> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-comments fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Messages"></i></dt> <dd>15</dd> </dl> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-thumbs-up fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Reaction score"></i></dt> <dd>2</dd> </dl> </div> <span class="message-userArrow"></span> </section> </div> <div class="message-cell message-cell--main"> <div class="message-main js-quickEditTarget"> <div class="message-content js-messageContent"> <div class="message-userContent lbContainer js-lbContainer " data-lb-id="post-6926869" data-lb-caption-desc="UFSJ · Aug 28, 2023 at 8:02 AM"> <article class="message-body js-selectToQuote"> <div class="googleads_fixed"> <script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-6580726045122001" crossorigin="anonymous"></script>  <ins class="adsbygoogle" style="display:block" data-ad-client="ca-pub-6580726045122001" data-ad-slot="3049969336" data-ad-format="auto" data-full-width-responsive="true"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script> </div> <div > <div class="bbWrapper">Hi guys.<br /> <br /> Using the Wang-Landau algorithm, I have tried to simulate the magnetic behavior of a bulk perovskite by the Monte Carlo method. I have used the JDoS description to build the Energy x magnetization phase space. By a referencing article, this magnetic system can be described by the Hamiltonian:<br /> H = - 2J<sub>1</sub> ∑ S<sub>i</sub> S<sub>j</sub> - 2J<sub>2</sub> ∑ S<sub>i</sub><br /> S<sub>k</sub> - D ∑ S<sub>i</sub> <sup>2</sup>, where J<sub>1</sub> is the exchange constant between two spins of the same basal plane (0.83 meV), J<sub>2</sub> is the exchange constant between two different basal planes (- 0.58 meV), D is the anisotropic constant (0.165 meV) and the experimental T<sub>N</sub> = 139.5 K. This compound is an A-type Néel antiferromagnetic. Below, I share my Wang-Landau program to obtain the density of states (actually to obtain the ln[g(E,m)]) written in Fortran 90. Can anyone point out where my error is? I am obtaining a phase transition temperature at 75 K.<br /> <br /> Thanks! <div class="bbCodeBlock bbCodeBlock--screenLimited bbCodeBlock--code language-fortran " data-xf-init="CMTV-code-block"> <div class="bbCodeBlock-header"> <div class="bbCodeBlock-title"> <span title="Fortran"> Wang-Landau JDoS: </span> </div> <div class="bbCodeBlock-actions"> <i class="fa--xf fal fa-expand-alt action action--expand action--hidden" aria-hidden="true" title="Expand" data-xf-init="tooltip" data-xf-click="CMTV-code-block-expand"></i> <i class="fa--xf fal fa-compress-alt action action--collapse action--hidden" aria-hidden="true" title="Collapse" data-xf-init="tooltip" data-xf-click="CMTV-code-block-collapse"></i> <i class="fa--xf fal fa-paste action action--copy" aria-hidden="true" title="Copy" data-xf-init="tooltip"></i> </div> </div> <div class="bbCodeBlock-content" dir="ltr"> <pre class="bbCodeCode line-numbers" dir="ltr" data-line="" data-xf-init="CMTV-code-block-extend" data-lang="fortran"><code>PROGRAM Perov_4est_JDoS IMPLICIT NONE INTEGER, PARAMETER :: lz = 20 ! lattice length INTEGER, PARAMETER :: ly = 20 INTEGER, PARAMETER :: lx = 20 INTEGER, PARAMETER :: n = lx*ly*lz ! number of spins INTEGER, PARAMETER :: ff = 25 ! number of loops applying the modification factor e^0.5 REAL, PARAMETER :: flat = 0.95 ! the flatness parameter INTEGER, PARAMETER :: cond = 1 ! if cond =1 the boundary conditions is ON, if cond = 0 is OFF REAL, PARAMETER :: J1 = 2*0.83 ! exchange constant in the same basal plane in units of de meV REAL, PARAMETER :: J2 = 2*(-0.58) ! exchange constant between basal planes in units of de meV REAL, PARAMETER :: D = 0.1*J1 ! anisotropic constant in units of meV REAL, PARAMETER :: E_max = n*((J1*16 - J2*8)/2 - D*4) ! maximum energy value INTEGER, PARAMETER :: bin_E = 10**4 ! maximum number of different energy values to be get INTEGER, PARAMETER :: bin_m = 10**4 ! maximum number of different magnetization values to be get INTEGER :: r, k, q, r1, r2, k1, k2, px, py, pz, pV, pG, pr, pf, ping, pong, idum, sf REAL :: Ei, Ef, mi, mf, E_latt, M_latt, E, m DOUBLE PRECISION :: test, E_fund, h_sum, f, ln_Ohm_fund INTEGER, DIMENSION (bin_E,bin_m) :: h, h_acum ! matrix Histograma and accumulated Histograma DOUBLE PRECISION, DIMENSION (bin_E,bin_m) :: g ! matrix of the log of density of states REAL, DIMENSION (bin_E) :: E_val ! array of energy values REAL, DIMENSION (bin_m) :: m_val ! array of magnetization values INTEGER, DIMENSION (n+1) :: s ! spin ! array os the values of the spin INTEGER, DIMENSION (n) :: sv1 ! at right ! arrays of the neighbor's position along the spin chain INTEGER, DIMENSION (n) :: sv2 ! at left INTEGER, DIMENSION (n) :: sv3 ! in the next line INTEGER, DIMENSION (n) :: sv4 ! in the bottom line INTEGER, DIMENSION (n) :: sv5 ! in the up basal plane INTEGER, DIMENSION (n) :: sv6 ! in the down basal plane CHARACTER(LEN = 70) :: txt REAL :: rd, xrand idum = 123456789 s(n+1) = 0 ! Array of first neighbors DO pz=1,lz DO py=1,ly DO px=1,lx r = px + lx*(py - 1) + lx*ly*(pz - 1) sv1(r) = r + 1 ! at right sv2(r) = r - 1 ! at left sv3(r) = r + lx ! in the next line sv4(r) = r - lx ! in the bottom line sv5(r) = r + lx*ly ! up sv6(r) = r - lx*ly ! down END DO END DO END DO! Boundary condition IF (cond==1) THEN ! boundary condition ON DO pz=1,lz DO py=1,ly DO px=1,lx r = px + lx*(py - 1) + lx*ly*(pz - 1) IF(px==lx) THEN sv1(r) = r - lx + 1 ! at right END IF IF(px==1) THEN sv2(r) = r + lx - 1 ! at left END IF IF(py==ly) THEN sv3(r) = r - lx*(ly - 1) ! in the next line END IF IF(py==1) THEN sv4(r) = r + lx*(ly - 1) ! in the line before END IFIF(pz==lz) THEN sv5(r) = r - lx*ly*(lz - 1) ! up END IF IF(pz==1) THEN sv6(r) = r + lx*ly*(lz - 1) ! down END IF END DO END DO END DOELSE IF (cond==0) THEN ! boundary condition OFF DO pz=1,lz DO py=1,ly DO px=1,lx r = px + lx*(py - 1) + lx*ly*(pz - 1) IF(px==1) THEN sv2(r) = n + 1 ! at left END IF IF(px==lx) THEN sv1(r) = n + 1 ! at right END IF IF(py==1) THEN sv4(r) = n + 1 ! in the line before END IF IF(py==ly) THEN sv3(r) = n + 1 ! in the next line END IF IF(pz==1) THEN sv5(r) = n + 1 ! up END IF IF(pz==lz) THEN sv6(r) = n + 1 ! down END IF END DO END DO END DO END IF !!!!! Building the phase space E x m and updating the ln[g(E,m)] and histogram DO r=1,bin_E DO k=1,bin_m g(r,k)= 1 h_acum(r,k) = 0 E_val(r) = 123456789 ! filling the energy and magnetization arrays with any wrong values. As a new state is observed, these values will be updating m_val(k) = 123456789 END DO END DO DO k=1,n ! defining values for the spin-lattice rd = xrand(idum) IF (rd<=0.2) THEN s(k) = - 2 ELSE IF ((0.2<rd).AND.(rd<=0.4)) THEN s(k) = - 1 ELSE IF ((0.4<rd).AND.(rd<=0.6)) THEN s(k) = 0 ELSE IF ((0.6<rd).AND.(rd<=0.8)) THEN s(k) = 1 ELSE IF (0.8<rd) THEN s(k) = 2 END IF END DO E_latt = 0 M_latt = 0 DO k=1,n ! obtaining the initial values of energy and magnetization of the chain E_latt = E_latt - s(k)*( J1*( s(sv1(k)) + s(sv2(k)) + s(sv3(k)) + s(sv4(k)) )/2 + J2*( s(sv5(k)) + s(sv6(k)) )/2 + D*s(k) ) M_latt = M_latt + s(k) END DO Ei = E_latt mi= M_latt E_val(1) = Ei m_val(1) = mi DO pf=1,ff ! defining the value of the modification factor f = exp(1.0)**( 1/(2**(pf - 1.0) ) ) DO r=1,bin_E DO k=1,bin_m h(r,k)= 0 ! histogram END DO END DO print*, 'pf-', pf ping = 0 DO WHILE (ping==0) ! the beginning of the loop responsible for the flatness test DO pV=1,n*10**6 ! Monte Carlo loops testing new configuration of the chain rd = xrand(idum) ! random choice of a spin "q" to be flipped q = NINT(n*rd) IF(q==0) THEN q = n END IF rd = xrand(idum) ! Analyzing the flip of the spin "q" IF (s(q)==-2) THEN IF (rd<=0.25) THEN sf = - 1 ELSE IF ((0.25<rd).AND.(rd<=0.5)) THEN sf = 0 ELSE IF ((0.5<rd).AND.(rd<=0.75)) THEN sf = 1 ELSE IF (0.75<rd) THEN sf = 2 END IF ELSE IF (s(q)==-1) THEN IF (rd<=0.25) THEN sf = - 2 ELSE IF ((0.25<rd).AND.(rd<=0.5)) THEN sf = 0 ELSE IF ((0.5<rd).AND.(rd<=0.75)) THEN sf = 1 ELSE IF (0.75<rd) THEN sf = 2 END IF ELSE IF (s(q)==0) THEN IF (rd<=0.25) THEN sf = - 2 ELSE IF ((0.25<rd).AND.(rd<=0.5)) THEN sf = - 1 ELSE IF ((0.5<rd).AND.(rd<=0.75)) THEN sf = 1 ELSE IF (0.75<rd) THEN sf = 2 END IF ELSE IF (s(q)==1) THEN IF (rd<=0.25) THEN sf = - 2 ELSE IF ((0.25<rd).AND.(rd<=0.5)) THEN sf = - 1 ELSE IF ((0.5<rd).AND.(rd<=0.75)) THEN sf = 0 ELSE IF (0.75<rd) THEN sf = 2 END IF ELSE IF (s(q)==2) THEN IF (rd<=0.25) THEN sf = - 2 ELSE IF ((0.25<rd).AND.(rd<=0.5)) THEN sf = - 1 ELSE IF ((0.5<rd).AND.(rd<=0.75)) THEN sf = 0 ELSE IF (0.75<rd) THEN sf = 1 END IF END IF ! Calculating the value of energy and magnetization of the possible final state with the flip of the spin "q" Ef = Ei - (sf - s(q))*( J1*( s(sv1(q)) + s(sv2(q)) + s(sv3(q)) + s(sv4(q)) ) + J2*( s(sv5(q)) + s(sv6(q)) ) ) & - D*(sf**2 - s(q)**2) mf = mi + (sf - s(q)) DO r=1,bin_E ! identifying the position of the final energy along the Energy values array IF (abs(E_val(r) - Ef) <= 0.001 ) THEN r2 = r GO TO 100 END IF END DO DO r=1,bin_E ! defining a position for the final energy along the Energy array, if it already not have been made IF (abs(E_val(r) - 123456789) <= 0.001) THEN E_val(r) = Ef r2 = r GO TO 100 END IF END DO 100 CONTINUE DO k=1,bin_m ! identifying the position of the final magnetization along the magnetization values array IF (abs(m_val(k) - mf) <= 0.001 ) THEN k2 = k GO TO 200 END IF END DO DO k=1,bin_m ! defining a position for the final magnetization along the magnetization array, if it already not have been made IF (abs(m_val(k) - 123456789) <= 0.001) THEN m_val(k) = mf k2 = k GO TO 200 END IF END DO 200 CONTINUE rd = xrand(idum) ! analyzing the possibility of changing from initial state to the final state and updating the histogram and density of states IF (exp(g(r1,k1) - g(r2,k2)) >= 1) THEN g(r2,k2) = g(r2,k2) + log(f) h(r2,k2) = h(r2,k2) + 1 h_acum(r2,k2) = h_acum(r2,k2) + 1 s(q) = sf r1 = r2 k1 = k2 ELSE IF (exp(g(r1,k1) - g(r2,k2)) >= rd) THEN g(r2,k2) = g(r2,k2) + log(f) h(r2,k2) = h(r2,k2) + 1 h_acum(r2,k2) = h_acum(r2,k2) + 1 s(q) = sf r1 = r2 k1 = k2 ELSE ! Keeping in the initial state and updating the histogram and density of states g(r1,k1) = g(r1,k1) + log(f) h(r1,k1) = h(r1,k1) + 1 h_acum(r1,k1) = h_acum(r1,k1) + 1 END IFEND DO ! end of pV loop !!!!!!!!!!!!!!! flatness test h_sum = 0 pr = 0 DO r=1,bin_E DO k=1,bin_m IF (h_acum(r,k)>0) THEN ! considering just visited states, that is, the states with accumulated histogram not zero pr = pr + 1 h_sum = h_sum + h(r,k) END IF END DO END DO pong = 0 DO r=1,bin_E DO k=1,bin_m IF (h_acum(r,k)>0) THEN test = h(r,k)/(h_sum/pr) IF (test < flat) THEN pong = pong + 1 END IF END IF END DO END DO ! if all considered states pass the flatness test, then "ping" changes to 1 and we go out of the flatness test, update the modification faction and repeat the process IF (pong == 0) THEN ping = 1 END IFEND DO ! final of the flatness loop END DO ! final of the modification factor loop !!!!!! Normalization of the density of states ln_Ohm_fund = 0 E_fund = E_max ! starting considering the smallest value of energy as the maximum possible value DO r=1,bin_E DO k=1,bin_m IF ((h_acum(r,k)>0).AND.(E_val(r) < E_fund)) THEN ! updating the smallest value of energy among the values computed E_fund = E_val(r) ln_Ohm_fund = g(r,k) END IF END DO END DO DO r=1,bin_E DO k=1,bin_m IF (h_acum(r,k)>0) THEN g(r,k) = g(r,k) - ln_Ohm_fund + log(1.0) ! Updating the value of the density of states END IF END DO END DO ! creating the output file with the energy and magnetization values and the respective ln[ g(E,m) ] WRITE(txt,"(f4.2,f5.2,f4.2,I3,I3,I3,I0)") J1, J2, flat, ly, lx, lz, cond WRITE(txt, "(A,f4.2,A,f5.2,A,f4.2,A,I3,A,I3,AI3,A,I0,A)") 'J1=',J1,'J2=',J2,'_ & <h>=',flat,'lx=',lx,'ly=',ly,'lz=',lz,'cond=',cond,'.dat' OPEN(2, FILE = trim(txt), STATUS = 'unknown') DO r=1,bin_E DO k=1,bin_m IF (h_acum(r,k)>0) THEN WRITE(2, *) E_val(r),';',m_val(k),';',g(r,k) END IF END DO END DOEND PROGRAM !cccccccccc Random function generator FUNCTION XRAND(IDUM) INTEGER IDUM REAL XRAND INTEGER, PARAMETER :: IM1=2147413563, IM2=2147413399, IMM1=IM1-1 INTEGER, PARAMETER :: IA1=40014,IA2=40692,IQ1=53661,IQ2=52774,IR1=12211,IR2=3791,NTAB=32,NDIV=1+IMM1/NTAB REAL, PARAMETER :: AM=1./IM1,EPS=1.2E-7,RNMX=1.-EPS INTEGER IDUM2,J,K,IV(NTAB),IY SAVE IV,IY,IDUM2 DATA IDUM2/123456719/,IV/NTAB*0/,IY/0/ IF (IDUM .LE. 0)THEN IDUM=MAX(-IDUM,1) IDUM2=IDUM DO J=NTAB+1,1,-1 K=IDUM/IQ1 IDUM=IA1*(IDUM-K*IQ1)-K*IR1 IF(IDUM .LT. 0)IDUM=IDUM+IM1 IF(J .LE. NTAB)IV(J)=IDUM END DO IY=IV(1) END IF K=IDUM/IQ1 IDUM=IA1*(IDUM-K*IQ1)-K*IR1 IF(IDUM .LT. 0)IDUM=IDUM+IM1 K=IDUM2/IQ2 IDUM2=IA2*(IDUM2-K*IQ2)-K*IR2 IF(IDUM2 .LT. 0)IDUM2=IDUM2+IM2 J= 1 + IY/NDIV IY=IV(J)-IDUM2 IV(J)=IDUM IF(IY .LT. 1)IY=IY+IMM1 XRAND=MIN(AM*IY,RNMX) RETURN END</code></pre> </div> <div class="bbCodeBlock-grip resizer--hidden" data-xf-init="CMTV-code-block-resizer"> <i class="fa--xf fal fa-grip-horizontal" aria-hidden="true"></i> </div> </div></div> </div> <div class="js-selectToQuoteEnd"> </div> </article> </div> <div class="message-lastEdit"> Last edited: <time class="u-dt" dir="auto" datetime="2023-08-28T09:22:05-0500" data-time="1693232525" data-date-string="Aug 28, 2023" data-time-string="9:22 AM" title="Aug 28, 2023 at 9:22 AM">Aug 28, 2023</time> </div> </div> <footer class="message-footer"> <div class="reactionsBar js-reactionsList "> </div> <div class="js-historyTarget message-historyTarget toggleTarget" data-href="trigger-href"></div> </footer> </div> </div> </div> </article>  <div class="message-cell message-cell--main" id="post-physorg"> <a href="https://phys.org/physics-news/materials/" target="_blank">Physics news</a> on Phys.org <ul class="phys_items"> <li><a href="https://phys.org/news/2024-11-discovery-van-hove-singularities-materials.html" target="_blank">Discovery of van Hove singularities could lead to novel materials with desirable quantum properties</a></li> <li><a href="https://phys.org/news/2024-11-molecule-durable-oleds-displays.html" target="_blank">New organic molecule design can lead to long-lasting, durable OLEDs for displays</a></li> <li><a href="https://phys.org/news/2024-11-topological-2d-materials-spiral-boundary.html" target="_blank">Researchers calculate topological numbers for 2D materials with spiral boundary conditions</a></li> </ul> </div> <article class="message message--post js-post js-inlineModContainer " data-author="berkeman" data-content="post-6926884" id="js-post-6926884" itemscope 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<li> #2 </li> </ul> </header> </div> <div class="message-inner"> <div class="message-cell message-cell--user"> <section class="message-user" itemprop="author" itemscope itemtype="https://schema.org/Person" itemid="https://www.physicsforums.com/members/berkeman.8921/"> <meta itemprop="url" content="https://www.physicsforums.com/members/berkeman.8921/" /> <div class="message-userDetails"> <span class="message-name"><a href="/members/berkeman.8921/" class="username " dir="auto" data-user-id="8921" data-xf-init="member-tooltip"><span class="username--staff username--moderator" itemprop="name">berkeman</span></a></span>    <div class="post-badges"> <div class="post-badge badge-mentor" data-xf-init="tooltip" title="PF Community Staff"> <i class="fa--xf fal fa-user-graduate" aria-hidden="true"></i><span> Mentor</span> </div> </div>  </div> <div class="message-userExtras"> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-comments fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Messages"></i></dt> <dd>68,297</dd> </dl> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-thumbs-up fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Reaction score"></i></dt> <dd>22,017</dd> </dl> </div> <span class="message-userArrow"></span> </section> </div> <div class="message-cell message-cell--main"> <div class="message-main js-quickEditTarget"> <div class="message-content js-messageContent"> <div class="message-userContent lbContainer js-lbContainer " data-lb-id="post-6926884" data-lb-caption-desc="berkeman · Aug 28, 2023 at 8:59 AM"> <article class="message-body js-selectToQuote"> <div itemprop="text"> <div class="bbWrapper"><blockquote data-attributes="member: 646881" data-quote="UFSJ" data-source="post: 6926869" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-title"> UFSJ said: </div> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> Hi guys.<br /> <br /> I have tried to simulate the magnetic behavior of a bulk perovskite by Monte Carlo method through the Wang-Landau algorithm. I have used the JDoS description of the phase space. By a reference article the magnetic system can be described by the hamiltonian: </div> </div> </blockquote>Hi Professor, it looks like your post got cut off. Can you try again?</div> </div> <div class="js-selectToQuoteEnd"> </div> </article> </div> </div> <footer class="message-footer"> <div class="message-microdata" itemprop="interactionStatistic" itemtype="https://schema.org/InteractionCounter" itemscope> <meta itemprop="userInteractionCount" content="0" /> <meta itemprop="interactionType" content="https://schema.org/LikeAction" /> </div> <div class="reactionsBar js-reactionsList "> </div> <div class="js-historyTarget message-historyTarget toggleTarget" data-href="trigger-href"></div> </footer> </div> </div> </div> </article>  <article class="message message--post js-post js-inlineModContainer " data-author="UFSJ" data-content="post-6926890" id="js-post-6926890" itemscope itemtype="https://schema.org/Comment" itemid="https://www.physicsforums.com/posts/6926890/"> <meta itemprop="parentItem" itemscope itemid="https://www.physicsforums.com/threads/monte-carlo-wang-landau_antiferromagnetic-perovskite.1055241/" /> <span class="u-anchorTarget" id="post-6926890"></span> <div class="message-header"> <header class="message-attribution message-attribution--split"> <ul class="message-attribution-main listInline "> <li class="u-concealed"> <time class="u-dt" dir="auto" datetime="2023-08-28T09:23:16-0500" data-time="1693232596" data-date-string="Aug 28, 2023" data-time-string="9:23 AM" title="Aug 28, 2023 at 9:23 AM" itemprop="datePublished">Aug 28, 2023</time> </li> </ul> <ul class="message-attribution-opposite message-attribution-opposite--list "> <li> <span style="cursor:pointer;" data-xf-init="share-tooltip" data-href="/posts/6926890/share" aria-label="Share" role="button" rel="nofollow"> <i class="fa--xf fal fa-share-alt" aria-hidden="true"></i> </span> </li> <li> #3 </li> </ul> </header> </div> <div class="message-inner"> <div class="message-cell message-cell--user"> <section class="message-user" itemprop="author" itemscope itemtype="https://schema.org/Person" itemid="https://www.physicsforums.com/members/ufsj.646881/"> <meta itemprop="url" content="https://www.physicsforums.com/members/ufsj.646881/" /> <div class="message-userDetails"> <span class="message-name"><span class="username " dir="auto" data-user-id="646881"><span itemprop="name">UFSJ</span></span></span>   <span class="threadstarter" data-xf-init="tooltip" title="Thread Starter"><i class="fal fa-user-edit"></i></span>   </div> <div class="message-userExtras"> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-comments fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Messages"></i></dt> <dd>15</dd> </dl> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-thumbs-up fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Reaction score"></i></dt> <dd>2</dd> </dl> </div> <span class="message-userArrow"></span> </section> </div> <div class="message-cell message-cell--main"> <div class="message-main js-quickEditTarget"> <div class="message-content js-messageContent"> <div class="message-userContent lbContainer js-lbContainer " data-lb-id="post-6926890" data-lb-caption-desc="UFSJ · Aug 28, 2023 at 9:23 AM"> <article class="message-body js-selectToQuote"> <div class="googleads_fixed"> <script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-6580726045122001" crossorigin="anonymous"></script>  <ins class="adsbygoogle" style="display:block" data-ad-client="ca-pub-6580726045122001" data-ad-slot="5961342082" data-ad-format="auto" data-full-width-responsive="true"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script> </div> <div itemprop="text"> <div class="bbWrapper"><blockquote data-attributes="member: 8921" data-quote="berkeman" data-source="post: 6926884" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-title"> berkeman said: </div> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> Hi Professor, it looks like your post got cut off. Can you try again? </div> </div> </blockquote>Thank by the alert. And now, still cut off?</div> </div> <div class="js-selectToQuoteEnd"> </div> </article> </div> </div> <footer class="message-footer"> <div class="message-microdata" itemprop="interactionStatistic" itemtype="https://schema.org/InteractionCounter" itemscope> <meta itemprop="userInteractionCount" content="1" /> <meta itemprop="interactionType" content="https://schema.org/LikeAction" /> </div> <div class="reactionsBar js-reactionsList is-active"> <ul class="reactionSummary"> <li><span class="reaction reaction--small reaction--1" data-reaction-id="1"><i aria-hidden="true"></i><img src="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" class="reaction-sprite js-reaction" alt="Like" title="Like" /></span></li> </ul> <span class="u-srOnly">Likes</span> <bdi>berkeman</bdi> </div> <div class="js-historyTarget message-historyTarget toggleTarget" data-href="trigger-href"></div> </footer> </div> </div> </div> </article>  <article class="message message--post js-post js-inlineModContainer " data-author="berkeman" data-content="post-6926895" id="js-post-6926895" itemscope itemtype="https://schema.org/Comment" itemid="https://www.physicsforums.com/posts/6926895/"> <meta itemprop="parentItem" itemscope itemid="https://www.physicsforums.com/threads/monte-carlo-wang-landau_antiferromagnetic-perovskite.1055241/" /> <span class="u-anchorTarget" id="post-6926895"></span> <div class="message-header"> <header class="message-attribution message-attribution--split"> <ul class="message-attribution-main listInline "> <li class="u-concealed"> <time class="u-dt" dir="auto" datetime="2023-08-28T09:29:26-0500" data-time="1693232966" data-date-string="Aug 28, 2023" data-time-string="9:29 AM" title="Aug 28, 2023 at 9:29 AM" itemprop="datePublished">Aug 28, 2023</time> </li> </ul> <ul class="message-attribution-opposite message-attribution-opposite--list "> <li> <span style="cursor:pointer;" data-xf-init="share-tooltip" data-href="/posts/6926895/share" aria-label="Share" role="button" rel="nofollow"> <i class="fa--xf fal fa-share-alt" aria-hidden="true"></i> </span> </li> <li> #4 </li> </ul> </header> </div> <div class="message-inner"> <div class="message-cell message-cell--user"> <section class="message-user" itemprop="author" itemscope itemtype="https://schema.org/Person" itemid="https://www.physicsforums.com/members/berkeman.8921/"> <meta itemprop="url" content="https://www.physicsforums.com/members/berkeman.8921/" /> <div class="message-userDetails"> <span class="message-name"><a href="/members/berkeman.8921/" class="username " dir="auto" data-user-id="8921" data-xf-init="member-tooltip"><span class="username--staff username--moderator" itemprop="name">berkeman</span></a></span>    <div class="post-badges"> <div class="post-badge badge-mentor" data-xf-init="tooltip" title="PF Community Staff"> <i class="fa--xf fal fa-user-graduate" aria-hidden="true"></i><span> Mentor</span> </div> </div>  </div> <div class="message-userExtras"> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-comments fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Messages"></i></dt> <dd>68,297</dd> </dl> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-thumbs-up fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Reaction score"></i></dt> <dd>22,017</dd> </dl> </div> <span class="message-userArrow"></span> </section> </div> <div class="message-cell message-cell--main"> <div class="message-main js-quickEditTarget"> <div class="message-content js-messageContent"> <div class="message-userContent lbContainer js-lbContainer " data-lb-id="post-6926895" data-lb-caption-desc="berkeman · Aug 28, 2023 at 9:29 AM"> <article class="message-body js-selectToQuote"> <div itemprop="text"> <div class="bbWrapper">Nope, looks fine now. <img src="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" class="smilie smilie--sprite smilie--sprite1" alt=":smile:" title="Smile :smile:" 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I have used the JDoS description to build the Energy x magnetization phase space. By a referencing article, this magnetic system can be described by the Hamiltonian:\nH = - 2J1 \u2211 Si Sj - 2J2 \u2211 Si\nSk - D \u2211 Si 2, where J1 is the exchange constant between two spins of the same basal plane (0.83 meV), J2 is the exchange constant between two different basal planes (- 0.58 meV), D is the anisotropic constant (0.165 meV) and the experimental TN = 139.5 K. This compound is an A-type N\u00e9el antiferromagnetic. Below, I share my Wang-Landau program to obtain the density of states (actually to obtain the ln[g(E,m)]) written in Fortran 90. Can anyone point out where my error is? I am obtaining a phase transition temperature at 75 K.\n\nThanks!\nPROGRAM Perov_4est_JDoS\nIMPLICIT NONE\n\nINTEGER, PARAMETER :: lz = 20 ! lattice length\nINTEGER, PARAMETER :: ly = 20\nINTEGER, PARAMETER :: lx = 20\nINTEGER, PARAMETER :: n = lx*ly*lz ! number of spins\nINTEGER, PARAMETER :: ff = 25 ! number of loops applying the modification factor e^0.5\n \nREAL, PARAMETER :: flat = 0.95 ! the flatness parameter\nINTEGER, PARAMETER :: cond = 1 ! if cond =1 the boundary conditions is ON, if cond = 0 is OFF\n\nREAL, PARAMETER :: J1 = 2*0.83 ! exchange constant in the same basal plane in units of de meV\nREAL, PARAMETER :: J2 = 2*(-0.58) ! exchange constant between basal planes in units of de meV\nREAL, PARAMETER :: D = 0.1*J1 ! anisotropic constant in units of meV\n\nREAL, PARAMETER :: E_max = n*((J1*16 - J2*8)/2 - D*4) ! maximum energy value\n\nINTEGER, PARAMETER :: bin_E = 10**4 ! maximum number of different energy values to be get\nINTEGER, PARAMETER :: bin_m = 10**4 ! maximum number of different magnetization values to be get\n\nINTEGER :: r, k, q, r1, r2, k1, k2, px, py, pz, pV, pG, pr, pf, ping, pong, idum, sf\nREAL :: Ei, Ef, mi, mf, E_latt, M_latt, E, m\nDOUBLE PRECISION :: test, E_fund, h_sum, f, ln_Ohm_fund\n\nINTEGER, DIMENSION (bin_E,bin_m) :: h, h_acum ! matrix Histograma and accumulated Histograma\nDOUBLE PRECISION, DIMENSION (bin_E,bin_m) :: g ! matrix of the log of density of states\nREAL, DIMENSION (bin_E) :: E_val ! array of energy values\nREAL, DIMENSION (bin_m) :: m_val ! array of magnetization values\n\nINTEGER, DIMENSION (n+1) :: s ! spin ! array os the values of the spin\n\nINTEGER, DIMENSION (n) :: sv1 ! at right ! arrays of the neighbor's position along the spin chain\nINTEGER, DIMENSION (n) :: sv2 ! at left\nINTEGER, DIMENSION (n) :: sv3 ! in the next line\nINTEGER, DIMENSION (n) :: sv4 ! in the bottom line\nINTEGER, DIMENSION (n) :: sv5 ! in the up basal plane\nINTEGER, DIMENSION (n) :: sv6 ! in the down basal plane\n\nCHARACTER(LEN = 70) :: txt\n\nREAL :: rd, xrand\nidum = 123456789\ns(n+1) = 0\n\n! Array of first neighbors\nDO pz=1,lz\nDO py=1,ly\nDO px=1,lx\nr = px + lx*(py - 1) + lx*ly*(pz - 1)\n\nsv1(r) = r + 1 ! at right\nsv2(r) = r - 1 ! at left\nsv3(r) = r + lx ! in the next line\nsv4(r) = r - lx ! in the bottom line\nsv5(r) = r + lx*ly ! up\nsv6(r) = r - lx*ly ! down\n\nEND DO\nEND DO\nEND DO! Boundary condition\nIF (cond==1) THEN ! boundary condition ON\nDO pz=1,lz\nDO py=1,ly\nDO px=1,lx\nr = px + lx*(py - 1) + lx*ly*(pz - 1)\n\nIF(px==lx) THEN\nsv1(r) = r - lx + 1 ! at right\nEND IF\nIF(px==1) THEN\nsv2(r) = r + lx - 1 ! at left\nEND IF\n\nIF(py==ly) THEN\nsv3(r) = r - lx*(ly - 1) ! in the next line\nEND IF\nIF(py==1) THEN\nsv4(r) = r + lx*(ly - 1) ! in the line before\nEND IFIF(pz==lz) THEN\nsv5(r) = r - lx*ly*(lz - 1) ! up\nEND IF\nIF(pz==1) THEN\nsv6(r) = r + lx*ly*(lz - 1) ! down\nEND IF\n\nEND DO\nEND DO\nEND DOELSE IF (cond==0) THEN ! boundary condition OFF\nDO pz=1,lz\nDO py=1,ly\nDO px=1,lx\nr = px + lx*(py - 1) + lx*ly*(pz - 1)\n\nIF(px==1) THEN\nsv2(r) = n + 1 ! at left\nEND IF\nIF(px==lx) THEN\nsv1(r) = n + 1 ! at right\nEND IF\n\nIF(py==1) THEN\nsv4(r) = n + 1 ! in the line before\nEND IF\nIF(py==ly) THEN\nsv3(r) = n + 1 ! in the next line\nEND IF\n\nIF(pz==1) THEN\nsv5(r) = n + 1 ! up\nEND IF\nIF(pz==lz) THEN\nsv6(r) = n + 1 ! down\nEND IF\n\nEND DO\nEND DO\nEND DO\n\nEND IF\n\n!!!!! Building the phase space E x m and updating the ln[g(E,m)] and histogram\nDO r=1,bin_E\nDO k=1,bin_m\n g(r,k)= 1\n h_acum(r,k) = 0\n E_val(r) = 123456789 ! filling the energy and magnetization arrays with any wrong values. As a new state is observed, these values will be updating\n m_val(k) = 123456789\nEND DO\nEND DO\nDO k=1,n ! defining values for the spin-lattice\nrd = xrand(idum)\n IF (rd<=0.2) THEN\n s(k) = - 2\n ELSE IF ((0.2<rd).AND.(rd<=0.4)) THEN\n s(k) = - 1\n ELSE IF ((0.4<rd).AND.(rd<=0.6)) THEN\n s(k) = 0\n ELSE IF ((0.6<rd).AND.(rd<=0.8)) THEN\n s(k) = 1\n ELSE IF (0.8<rd) THEN\n s(k) = 2\n END IF\nEND DO\n\nE_latt = 0\nM_latt = 0\nDO k=1,n ! obtaining the initial values of energy and magnetization of the chain\n E_latt = E_latt - s(k)*( J1*( s(sv1(k)) + s(sv2(k)) + s(sv3(k)) + s(sv4(k)) )/2 + J2*( s(sv5(k)) + s(sv6(k)) )/2 + D*s(k) )\n M_latt = M_latt + s(k)\nEND DO\nEi = E_latt\nmi= M_latt\nE_val(1) = Ei\nm_val(1) = mi\nDO pf=1,ff ! defining the value of the modification factor\nf = exp(1.0)**( 1/(2**(pf - 1.0) ) )\n\n DO r=1,bin_E\n DO k=1,bin_m\n h(r,k)= 0 ! histogram\n END DO\n END DO\n\nprint*, 'pf-', pf\nping = 0\nDO WHILE (ping==0) ! the beginning of the loop responsible for the flatness test\n\nDO pV=1,n*10**6 ! Monte Carlo loops testing new configuration of the chain\n\nrd = xrand(idum) ! random choice of a spin \"q\" to be flipped\nq = NINT(n*rd)\nIF(q==0) THEN\n q = n\nEND IF\n\nrd = xrand(idum) ! Analyzing the flip of the spin \"q\"\nIF (s(q)==-2) THEN\n IF (rd<=0.25) THEN\n sf = - 1\n ELSE IF ((0.25<rd).AND.(rd<=0.5)) THEN\n sf = 0\n ELSE IF ((0.5<rd).AND.(rd<=0.75)) THEN\n sf = 1\n ELSE IF (0.75<rd) THEN\n sf = 2\n END IF\n \nELSE IF (s(q)==-1) THEN\n IF (rd<=0.25) THEN\n sf = - 2\n ELSE IF ((0.25<rd).AND.(rd<=0.5)) THEN\n sf = 0\n ELSE IF ((0.5<rd).AND.(rd<=0.75)) THEN\n sf = 1\n ELSE IF (0.75<rd) THEN\n sf = 2\n END IF\n\nELSE IF (s(q)==0) THEN\n IF (rd<=0.25) THEN\n sf = - 2\n ELSE IF ((0.25<rd).AND.(rd<=0.5)) THEN\n sf = - 1\n ELSE IF ((0.5<rd).AND.(rd<=0.75)) THEN\n sf = 1\n ELSE IF (0.75<rd) THEN\n sf = 2\n END IF\n\nELSE IF (s(q)==1) THEN\n IF (rd<=0.25) THEN\n sf = - 2\n ELSE IF ((0.25<rd).AND.(rd<=0.5)) THEN\n sf = - 1\n ELSE IF ((0.5<rd).AND.(rd<=0.75)) THEN\n sf = 0\n ELSE IF (0.75<rd) THEN\n sf = 2\n END IF\n\nELSE IF (s(q)==2) THEN\n IF (rd<=0.25) THEN\n sf = - 2\n ELSE IF ((0.25<rd).AND.(rd<=0.5)) THEN\n sf = - 1\n ELSE IF ((0.5<rd).AND.(rd<=0.75)) THEN\n sf = 0\n ELSE IF (0.75<rd) THEN\n sf = 1\n END IF\n\nEND IF\n ! Calculating the value of energy and magnetization of the possible final state with the flip of the spin \"q\"\nEf = Ei - (sf - s(q))*( J1*( s(sv1(q)) + s(sv2(q)) + s(sv3(q)) + s(sv4(q)) ) + J2*( s(sv5(q)) + s(sv6(q)) ) ) &\n- D*(sf**2 - s(q)**2)\nmf = mi + (sf - s(q)) \n DO r=1,bin_E ! identifying the position of the final energy along the Energy values array\n IF (abs(E_val(r) - Ef) <= 0.001 ) THEN\n r2 = r\n GO TO 100\n END IF\n END DO\n\n DO r=1,bin_E ! defining a position for the final energy along the Energy array, if it already not have been made\n IF (abs(E_val(r) - 123456789) <= 0.001) THEN\n E_val(r) = Ef\n r2 = r\n GO TO 100\n END IF\n END DO\n100 CONTINUE\n\n DO k=1,bin_m ! identifying the position of the final magnetization along the magnetization values array\n IF (abs(m_val(k) - mf) <= 0.001 ) THEN\n k2 = k\n GO TO 200\n END IF\n END DO\n\n DO k=1,bin_m ! defining a position for the final magnetization along the magnetization array, if it already not have been made\n IF (abs(m_val(k) - 123456789) <= 0.001) THEN\n m_val(k) = mf\n k2 = k\n GO TO 200\n END IF\n END DO\n200 CONTINUE rd = xrand(idum) ! analyzing the possibility of changing from initial state to the final state and updating the histogram and density of states\n IF (exp(g(r1,k1) - g(r2,k2)) >= 1) THEN\n g(r2,k2) = g(r2,k2) + log(f)\n h(r2,k2) = h(r2,k2) + 1\n h_acum(r2,k2) = h_acum(r2,k2) + 1\n s(q) = sf\n r1 = r2\n k1 = k2\n ELSE IF (exp(g(r1,k1) - g(r2,k2)) >= rd) THEN\n g(r2,k2) = g(r2,k2) + log(f)\n h(r2,k2) = h(r2,k2) + 1\n h_acum(r2,k2) = h_acum(r2,k2) + 1\n s(q) = sf\n r1 = r2\n k1 = k2\n ELSE ! Keeping in the initial state and updating the histogram and density of states\n g(r1,k1) = g(r1,k1) + log(f)\n h(r1,k1) = h(r1,k1) + 1\n h_acum(r1,k1) = h_acum(r1,k1) + 1\n END IFEND DO ! end of pV loop\n\n!!!!!!!!!!!!!!! flatness test\n h_sum = 0\n pr = 0\n DO r=1,bin_E\n DO k=1,bin_m\n IF (h_acum(r,k)>0) THEN ! considering just visited states, that is, the states with accumulated histogram not zero\n pr = pr + 1\n h_sum = h_sum + h(r,k)\n END IF\n END DO\n END DO\n\n pong = 0 \n DO r=1,bin_E\n DO k=1,bin_m\n IF (h_acum(r,k)>0) THEN\n test = h(r,k)/(h_sum/pr)\n IF (test < flat) THEN\n pong = pong + 1\n END IF\n END IF\n END DO\n END DO\n! if all considered states pass the flatness test, then \"ping\" changes to 1 and we go out of the flatness test, update the modification faction and repeat the process\n IF (pong == 0) THEN \n ping = 1\n END IFEND DO ! final of the flatness loop\n\nEND DO ! final of the modification factor loop\n!!!!!! Normalization of the density of states\n\nln_Ohm_fund = 0\nE_fund = E_max ! starting considering the smallest value of energy as the maximum possible value\nDO r=1,bin_E\nDO k=1,bin_m\n IF ((h_acum(r,k)>0).AND.(E_val(r) < E_fund)) THEN ! updating the smallest value of energy among the values computed\n E_fund = E_val(r)\n ln_Ohm_fund = g(r,k)\n END IF\nEND DO\nEND DO\n\nDO r=1,bin_E\nDO k=1,bin_m\n IF (h_acum(r,k)>0) THEN\n g(r,k) = g(r,k) - ln_Ohm_fund + log(1.0) ! Updating the value of the density of states\n END IF\nEND DO\nEND DO\n\n! creating the output file with the energy and magnetization values and the respective ln[ g(E,m) ]\nWRITE(txt,\"(f4.2,f5.2,f4.2,I3,I3,I3,I0)\") J1, J2, flat, ly, lx, lz, cond\nWRITE(txt, \"(A,f4.2,A,f5.2,A,f4.2,A,I3,A,I3,AI3,A,I0,A)\") 'J1=',J1,'J2=',J2,'_ &\n<h>=',flat,'lx=',lx,'ly=',ly,'lz=',lz,'cond=',cond,'.dat'\nOPEN(2, FILE = trim(txt), STATUS = 'unknown')\n DO r=1,bin_E\n DO k=1,bin_m\n IF (h_acum(r,k)>0) THEN\n WRITE(2, *) E_val(r),';',m_val(k),';',g(r,k)\n END IF\n END DO\n END DOEND PROGRAM\n\n!cccccccccc Random function generator\n\n FUNCTION XRAND(IDUM)\n INTEGER IDUM\n REAL XRAND\n INTEGER, PARAMETER :: IM1=2147413563, IM2=2147413399, IMM1=IM1-1\n INTEGER, PARAMETER :: IA1=40014,IA2=40692,IQ1=53661,IQ2=52774,IR1=12211,IR2=3791,NTAB=32,NDIV=1+IMM1/NTAB\n REAL, PARAMETER :: AM=1./IM1,EPS=1.2E-7,RNMX=1.-EPS\n INTEGER IDUM2,J,K,IV(NTAB),IY\n SAVE IV,IY,IDUM2\n DATA IDUM2/123456719/,IV/NTAB*0/,IY/0/\n IF (IDUM .LE. 0)THEN\n IDUM=MAX(-IDUM,1)\n IDUM2=IDUM\n DO J=NTAB+1,1,-1\n K=IDUM/IQ1\n IDUM=IA1*(IDUM-K*IQ1)-K*IR1\n IF(IDUM .LT. 0)IDUM=IDUM+IM1\n IF(J .LE. NTAB)IV(J)=IDUM\n END DO\n IY=IV(1)\n END IF\n K=IDUM/IQ1\n IDUM=IA1*(IDUM-K*IQ1)-K*IR1\n IF(IDUM .LT. 0)IDUM=IDUM+IM1\n K=IDUM2/IQ2\n IDUM2=IA2*(IDUM2-K*IQ2)-K*IR2\n IF(IDUM2 .LT. 0)IDUM2=IDUM2+IM2\n J= 1 + IY/NDIV\n IY=IV(J)-IDUM2\n IV(J)=IDUM\n IF(IY .LT. 1)IY=IY+IMM1 XRAND=MIN(AM*IY,RNMX)\n RETURN\n END" }, "publisher": { "@type": "Organization", "name": "Physics Forums: Science Discussion, Homework Help, Articles", "alternateName": "Physics Forums", "description": "Join Physics Forums, where students, scientists, and enthusiasts come together to explore and discuss the current understanding and practice of various scientific fields.", "url": "https://www.physicsforums.com", "logo": "https://www.physicsforums.com/styles/physicsforums/images/physics-forums-logo-og.png" } } </script> <script type="text/javascript" src="https://www.physicsforums.com/copyright.js" defer></script> <script> function parseNewPost(postid) { var newpost = document.getElementById("js-post-" + postid), npa = [newpost]; MathJax.typeset(npa); } function parsePreview() { var preview = document.getElementsByClassName("xfPreview"); MathJax.typeset(preview); } function parseNewConversationPost(postid) { var newpost = document.getElementsByClassName("convMessage-" + postid); MathJax.typeset(newpost); } function parseNewProfilePost(postid) { var newpost = document.getElementById("js-profilePost-" + postid), npa = [newpost]; MathJax.typeset(npa); } function parseTooltip() { MathJax.typeset(); } </script> </body> </html>

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Monte Carlo Wang-Landau_antiferromagnetic perovskite