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The topological susceptibility Xt is measured directly, and by the slab method, which is based on the topological content of sub-volumes (“slabs”) and estimates Xt even when the system remains trapped in a fixed topological sector. The results obtained by both methods are essentially consistent, but the impact of the Gradient Flow on the characteristic quantity of the slab method seems to be different in 2-flavour QCD and in the 2d O(3) model. In the latter model, we further address the question whether or not the Gradient Flow leads to a finite continuum limit of the topological susceptibility (rescaled by the correlation length squared, ξ2). This ongoing study is based on direct measurements of Xt in L × L lattices, at L/ξ ≃6. We study the impact of the Gradient Flow on the topology in various models of lattice field theory. The topological susceptibility $\chi_{\rm t}$ is measured directly, and by the slab method, which is based on the topological content of sub-volumes ("slabs") and estimates $\chi_{\rm t}$ even when the system remains trapped in a fixed topological sector. The results obtained by both methods are essentially consistent, but the impact of the Gradient Flow on the characteristic quantity of the slab method seems to be different in 2-flavour QCD and in the 2d O(3) model. In the latter model, we further address the question whether or not the Gradient Flow leads to a finite continuum limit of the topological susceptibility (rescaled by the correlation length squared, $\xi^{2}$). This ongoing study is based on direct measurements of $\chi_{\rm t}$ in $L \times L$ lattices, at $L/\xi \simeq 6$. Mejía-Díaz, Héctor; Bietenholz, Wolfgang; Cichy, Krzysztof; de Forcrand, Philippe; Dromard, Arthur; Gerber, Urs; Sandoval, Ilya Orson" /> <meta name="keywords" content="CERN Document Server, WebSearch, CERN Document Server" /> <script type="text/javascript" src="https://cds.cern.ch/js/jquery.min.js"></script>  <link rel="stylesheet" href="https://cds.cern.ch/img/webnews.css" type="text/css" />  <script type="text/javascript" src="https://cds.cern.ch/js/webnews.js?v=20131009"></script> <meta property="fb:app_id" content="137353533001720"/>  <meta content="arXiv : Topological Susceptibility under Gradient Flow" name="citation_title" /> <meta content="Mejía-Díaz, Héctor" name="citation_author" /> <meta content="Cichy, Krzysztof" name="citation_author" /> <meta content="Dromard, Arthur" name="citation_author" /> <meta content="Gerber, Urs" name="citation_author" /> <meta content="Sandoval, Ilya Orson" name="citation_author" /> <meta content="Bietenholz, Wolfgang" name="citation_author" /> <meta content="de Forcrand, Philippe" name="citation_author" /> <meta content="10.1051/epjconf/201817511024" name="citation_doi" /> <meta content="EPJ Web Conf." name="citation_journal_title" /> <meta content="175" name="citation_volume" /> <meta content="11024" name="citation_firstpage" /> <meta content="2017/12/04" name="citation_publication_date" /> <meta name="citation_online_date" content="2017/12/20"> <meta content="arXiv:1712.01395" name="citation_technical_report_number" /> <meta content="10.1051/epjconf/201817511024" name="citation_doi" /> <meta name="citation_pdf_url" content="https://cds.cern.ch/record/2298635/files/arXiv:1712.01395.pdf" /> <meta name="citation_pdf_url" content="https://cds.cern.ch/record/2298635/files/epjconf_lattice2018_11024.pdf" />  <meta content="Topological Susceptibility under Gradient Flow" property="og:title" /> <meta content="arXiv" property="og:title" /> <meta content="website" property="og:type" /> <meta content="website" property="og:type" /> <meta content="https://cds.cern.ch/record/2298635" property="og:url" /> <meta name="twitter:image" content="https://cds.cern.ch/record/2298635/files/reference_nogrid-cropped.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2298635/files/reference_nogrid-cropped.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2298635/files/reference_nogrid-cropped.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2298635/files/QCDchit-cropped.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2298635/files/QCDchit-cropped.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2298635/files/qprime_vs_x_L120-cropped.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2298635/files/qprime_vs_x_L120-cropped.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2298635/files/chitGFslabB2L100c-cropped.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2298635/files/chitGFslabB2L100c-cropped.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2298635/files/ascenso_nogrid-cropped.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2298635/files/ascenso_nogrid-cropped.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2298635/files/CorrelFunc_L120_v3-cropped.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2298635/files/CorrelFunc_L120_v3-cropped.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2298635/files/descenso_reversed-cropped.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2298635/files/descenso_reversed-cropped.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2298635/files/cst_t0-cropped.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2298635/files/cst_t0-cropped.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2298635/files/chi_vs_t_L120-cropped.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2298635/files/chi_vs_t_L120-cropped.png" /> <meta property="og:image" content="https://cds.cern.ch/record/2298635/files/slabB2L100Q2meas2e6-cropped.png" /> <meta property="og:image:secure_url" content="https://cds.cern.ch/record/2298635/files/slabB2L100Q2meas2e6-cropped.png" /> <meta content="CERN Document Server" property="og:site_name" /> <meta content="We study the impact of the Gradient Flow on the topology in various models of lattice field theory. The topological susceptibility Xt is measured directly, and by the slab method, which is based on the topological content of sub-volumes (“slabs”) and estimates Xt even when the system remains trapped in a fixed topological sector. The results obtained by both methods are essentially consistent, but the impact of the Gradient Flow on the characteristic quantity of the slab method seems to be different in 2-flavour QCD and in the 2d O(3) model. In the latter model, we further address the question whether or not the Gradient Flow leads to a finite continuum limit of the topological susceptibility (rescaled by the correlation length squared, ξ2). This ongoing study is based on direct measurements of Xt in L × L lattices, at L/ξ ≃6." property="og:description" /> <meta content="arXiv" property="og:description" /> <meta content="We study the impact of the Gradient Flow on the topology in various models of lattice field theory. The topological susceptibility $\chi_{\rm t}$ is measured directly, and by the slab method, which is based on the topological content of sub-volumes (&quot;slabs&quot;) and estimates $\chi_{\rm t}$ even when the system remains trapped in a fixed topological sector. The results obtained by both methods are essentially consistent, but the impact of the Gradient Flow on the characteristic quantity of the slab method seems to be different in 2-flavour QCD and in the 2d O(3) model. In the latter model, we further address the question whether or not the Gradient Flow leads to a finite continuum limit of the topological susceptibility (rescaled by the correlation length squared, $\xi^{2}$). This ongoing study is based on direct measurements of $\chi_{\rm t}$ in $L \times L$ lattices, at $L/\xi \simeq 6$." property="og:description" /> <meta content="EDP Sciences" property="og:description" />  <meta content="summary" name="twitter:card" /> <meta content="summary" name="twitter:card" /> <style></style> </head> <body class="CERN32Document32Server search" lang="ru">  <div id="cern-toolbar"> <h1><a href="http://cern.ch" title="CERN">CERN <span>Accelerating science</span></a></h1> <ul> <li class="cern-accountlinks"><a class="cern-account" href="https://cds.cern.ch/youraccount/login?ln=ru&referer=https%3A//cds.cern.ch/record/2298635/export/hm%3Fln%3Dru" title="Sign in to your CERN account">Sign in</a></li> <li><a class="cern-directory" href="http://cern.ch/directory" title="Search CERN resources and browse the directory">Directory</a></li> </ul> </div>   <div role="banner" class="clearfix" id="header"> <div class="header-inner inner"> <hgroup class="clearfix"> <h2 id="site-name"> <a rel="home" title="Home" href="/"><span>CERN Document Server</span></a> </h2> <h3 id="site-slogan">Access articles, reports and multimedia content in HEP</h3> </hgroup> <div role="navigation" id="main-navigation" class="cdsmenu"> <h2 class="element-invisible">Main menu</h2><ul class="links inline clearfix"> <li class="menu-386 first active-trail"><a class="active-trail" href="https://cds.cern.ch/?ln=ru">Искать</a></li> <li class="menu-444 "><a class="" title="" href="https://cds.cern.ch/submit?ln=ru">Внести</a></li> <li class="menu-426 "><a class="" href="https://cds.cern.ch/help/?ln=ru">Помощь</a></li> <li class="leaf hassubcdsmenu"> <a hreflang="en" class="header" href="https://cds.cern.ch/youraccount/display?ln=ru">Персонализовать</a> <ul class="subsubcdsmenu"><li><a href="https://cds.cern.ch/youralerts/list?ln=ru">Ваши оповещения</a></li><li><a href="https://cds.cern.ch/yourbaskets/display?ln=ru">Ваши книжные полки</a></li><li><a href="https://cds.cern.ch/yourcomments?ln=ru">Your comments</a></li><li><a href="https://cds.cern.ch/youralerts/display?ln=ru">Ваши поисковые запросы</a></li></ul></li> </ul> </div> </div> </div>  <table class="navtrailbox"> <tr> <td class="navtrailboxbody"> <a href="/?ln=ru" class="navtrail">Главная страница</a> > <a class="navtrail" href="/record/2298635">Topological Susceptibility under Gradient Flow</a> > HTML MARC </td> </tr> </table> </div> <div class="pagebody"><div class="pagebodystripemiddle"> <pre style="margin: 1em 0px;">002298635 001__ 2298635 002298635 005__ 20230314175118.0 002298635 0248_ $$aoai:cds.cern.ch:2298635$$pcerncds:CERN$$pcerncds:CERN:FULLTEXT$$pcerncds:FULLTEXT 002298635 0247_ $$2DOI$$9bibmatch$$a10.1051/epjconf/201817511024 002298635 037__ $$9arXiv$$aarXiv:1712.01395$$chep-lat 002298635 035__ $$9arXiv$$aoai:arXiv.org:1712.01395 002298635 035__ $$9Inspire$$aoai:inspirehep.net:1641083$$d2023-03-06T19:16:53Z$$h2023-03-14T15:04:38Z$$mmarcxml$$ttrue$$uhttps://inspirehep.net/api/oai2d 002298635 035__ $$9Inspire$$a1641083 002298635 041__ $$aeng 002298635 100__ $$aMejía-Díaz, Héctor$$uMexico U., ICN$$vInstituto de Ciencias Nucleares, Universidad Nacional Autónoma de México A.P. 70-543, C.P. 04510 Ciudad de México, Mexico 002298635 245__ $$9arXiv$$aTopological Susceptibility under Gradient Flow 002298635 246__ $$9arXiv$$aTopological Susceptibility under Gradient Flow 002298635 269__ $$c2017-12-04 002298635 260__ $$c2018 002298635 300__ $$a8 p 002298635 500__ $$9arXiv$$a8 pages, LaTex, 5 figures, talk presented at the 35th International Symposium on Lattice Field Theory, June 18-24, 2017, Granada, Spain 002298635 520__ $$9EDP Sciences$$aWe study the impact of the Gradient Flow on the topology in various models of lattice field theory. The topological susceptibility Xt is measured directly, and by the slab method, which is based on the topological content of sub-volumes (“slabs”) and estimates Xt even when the system remains trapped in a fixed topological sector. The results obtained by both methods are essentially consistent, but the impact of the Gradient Flow on the characteristic quantity of the slab method seems to be different in 2-flavour QCD and in the 2d O(3) model. In the latter model, we further address the question whether or not the Gradient Flow leads to a finite continuum limit of the topological susceptibility (rescaled by the correlation length squared, ξ2). This ongoing study is based on direct measurements of Xt in L × L lattices, at L/ξ ≃6. 002298635 520__ $$9arXiv$$aWe study the impact of the Gradient Flow on the topology in various models of lattice field theory. The topological susceptibility $\chi_{\rm t}$ is measured directly, and by the slab method, which is based on the topological content of sub-volumes ("slabs") and estimates $\chi_{\rm t}$ even when the system remains trapped in a fixed topological sector. The results obtained by both methods are essentially consistent, but the impact of the Gradient Flow on the characteristic quantity of the slab method seems to be different in 2-flavour QCD and in the 2d O(3) model. In the latter model, we further address the question whether or not the Gradient Flow leads to a finite continuum limit of the topological susceptibility (rescaled by the correlation length squared, $\xi^{2}$). This ongoing study is based on direct measurements of $\chi_{\rm t}$ in $L \times L$ lattices, at $L/\xi \simeq 6$. 002298635 540__ $$aarXiv nonexclusive-distrib. 1.0$$barXiv$$uhttp://arxiv.org/licenses/nonexclusive-distrib/1.0/ 002298635 540__ $$9EDP Sciences$$aCC-BY-4.0$$uhttp://creativecommons.org/licenses/by/4.0/ 002298635 65017 $$2arXiv$$ahep-lat 002298635 65017 $$2SzGeCERN$$aParticle Physics - Lattice 002298635 690C_ $$aCERN 002298635 690C_ $$aARTICLE 002298635 700__ $$aBietenholz, Wolfgang$$uMexico U., ICN$$vInstituto de Ciencias Nucleares, Universidad Nacional Autónoma de México A.P. 70-543, C.P. 04510 Ciudad de México, Mexico 002298635 700__ $$aCichy, Krzysztof$$uMickiewicz U., Poznan$$uFrankfurt U.$$vFaculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznán, Poland$$vGoethe-Universität Frankfurt am Main, Institut für Theoretische Physik Max-von-Laue-Straße 1, 60438 Frankfurt am Main, Germany 002298635 700__ $$ade Forcrand, Philippe$$uZurich, ETH$$uCERN$$vCERN, Theory Division, CH-1211 Genève 23, Switzerland$$vInstitut für Theoretische Physik, ETH Zürich, Wolfgang-Pauli-Strasse 27, CH–8093 Zürich, Switzerland 002298635 700__ $$aDromard, Arthur$$uRegensburg U.$$vInstitut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany 002298635 700__ $$aGerber, Urs$$uIFM-UMSNH, Michoacan$$uMexico U., ICN$$vInstituto de Ciencias Nucleares, Universidad Nacional Autónoma de México A.P. 70-543, C.P. 04510 Ciudad de México, Mexico$$vInstituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo Edificio C-3, Apdo. Postal 2-82, C.P. 58040, Morelia, Michoacán, Mexico 002298635 700__ $$aSandoval, Ilya Orson$$uMexico U., ICN$$vInstituto de Ciencias Nucleares, Universidad Nacional Autónoma de México A.P. 70-543, C.P. 04510 Ciudad de México, Mexico 002298635 773__ $$c11024$$pEPJ Web Conf.$$v175$$wC17-06-18.1$$y2018 002298635 8564_ $$81375166$$s4698$$uhttps://cds.cern.ch/record/2298635/files/QCDchit-cropped.png$$y00001 On the left: the expectation value $\la q{'}^{2} \ra$, as a function of the parameter $x = V_{\rm slab}/V$, in 2-flavour QCD, in the sector $|Q|=1$. Combined fits to eq.\ (\ref{extend}), in the sectors $|Q|\leq 2$, at different instances of the GF time, lead to the results for the topological susceptibility $\chi_{\rm t}$ in the plot on the right. They agree with a direct measurement, and with the method of Ref.\ \cite{AFHO} (AFHO method).Caption not extracted 002298635 8564_ $$81375167$$s19850$$uhttps://cds.cern.ch/record/2298635/files/qprime_vs_x_L120-cropped.png$$y00002 width=7cm,clip 002298635 8564_ $$81375168$$s16457$$uhttps://cds.cern.ch/record/2298635/files/chitGFslabB2L100c-cropped.png$$y00005 The slab method in the 1d O(2) model: at short GF times, $\la q{'}^{2} \ra (x)$ (on the left) can be fitted to eq.\ (\ref{predict}), but long flow times require an extension to eq.\ (\ref{extend}), and the exclusion of $x \gtapprox 0$ and $x \ltapprox 1$ from the fit. After a long flow time, the sector $Q=0$ provides the best results for $\chi_{\rm t}$, as the plot on the right shows.Caption not extracted 002298635 8564_ $$81375169$$s3535$$uhttps://cds.cern.ch/record/2298635/files/ascenso_nogrid-cropped.png$$y00009 Left: the GF time evolution of the term $\chi_{\rm t} \xi^{2}$ in nine $L \times L$ lattices, in each case at $L \simeq 6 \xi$. In large volumes we observe a rapid decrease at an early stage of the GF; this can be interpreted as the destruction of numerous small dislocations. Right: in the range $t=0 \dots 6 t_{0}$, the quantity $\chi_{\rm t} \xi^{2}$ does not seem to attain any finite continuum value as we approach the continuum (increasing $\xi$).Caption not extracted 002298635 8564_ $$81375170$$s54848$$uhttps://cds.cern.ch/record/2298635/files/cst_t0-cropped.png$$y00000 width=7cm,clipwidth=7.1cm,clip 002298635 8564_ $$81375171$$s4925$$uhttps://cds.cern.ch/record/2298635/files/descenso_reversed-cropped.png$$y00008 width=7cm,clip 002298635 8564_ $$81375172$$s6600$$uhttps://cds.cern.ch/record/2298635/files/reference_nogrid-cropped.png$$y00006 width=7cm,clip 002298635 8564_ $$81375173$$s9128$$uhttps://cds.cern.ch/record/2298635/files/chi_vs_t_L120-cropped.png$$y00003 On the left: the quantity $\la q{'}^{2} \ra (x)$, in the 2d O(3) model, in the sector $|Q|=1$, with and without GF. Fits to eq.\ (\ref{predict}), in the sectors $|Q|=0,\, 1,\, 2$, yield the results for $\chi_{\rm t}$, which are shown on the right. They are close to each other, and to the values from direct measurement (the GF drives them slightly apart).Caption not extracted 002298635 8564_ $$81375174$$s26252$$uhttps://cds.cern.ch/record/2298635/files/slabB2L100Q2meas2e6-cropped.png$$y00004 width=7cm,clip 002298635 8564_ $$81375175$$s18576$$uhttps://cds.cern.ch/record/2298635/files/CorrelFunc_L120_v3-cropped.png$$y00007 The 2d O(3) model under GF: on the left, the term $\la E \ra t$, which fixes a GF time unit $t_{0}$ (in lattice units) by the condition $\la E \ra \, t_{0}= 0.08$. On the right: the correlation function $C(r)$ at $t= 0,\, 4t_{0}, \, 8t_{0}$. At fixed distance $r$ the GF moves it up, but the correlation length $\xi$ remains practically constant.Caption not extracted 002298635 8564_ $$81375176$$s1324953$$uhttps://cds.cern.ch/record/2298635/files/arXiv:1712.01395.pdf 002298635 8564_ $$81395356$$s878592$$uhttps://cds.cern.ch/record/2298635/files/epjconf_lattice2018_11024.pdf$$yFulltext 002298635 960__ $$a13 002298635 962__ $$b2683005$$k11024$$ngranada20170618 002298635 980__ $$aConferencePaper 002298635 980__ $$aARTICLE</pre></div></div> <footer id="footer" class="pagefooter clearfix">  <div class="pagefooterstripeleft"> CERN Document Server :: <a class="footer" href="https://cds.cern.ch/?ln=ru">Искать</a> :: <a class="footer" href="https://cds.cern.ch/submit?ln=ru">Внести</a> :: <a class="footer" href="https://cds.cern.ch/youraccount/display?ln=ru">Персонализовать</a> :: <a class="footer" href="https://cds.cern.ch/help/?ln=ru">Помощь</a> :: <a class="footer" href="https://cern.service-now.com/service-portal?id=privacy_policy&se=CDS-Service" target="_blank">Privacy Notice</a> <br /> Развиваемое <a class="footer" href="http://invenio-software.org/">Invenio</a> <br /> Поддерживает <a class="footer" href="https://cern.service-now.com/service-portal?id=service_element&name=CDS-Service">CDS Service</a> - Need help? 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