Using zeros of the canonical partition function map to detect signatures of a Berezinskii-Kosterlitz-Thouless transition

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• 作者：J.C.S. Rocha^a ; ^b ; ^{jcsrocha@iceb.ufop.br" class="auth_mail" title="E-mail the corresponding author} ; L.A.S. Mó ; l^a ; ^{lucasmol@fisica.ufmg.br" class="auth_mail" title="E-mail the corresponding author} ; B.V. Costa^a ; ^{bvc@fisica.ufmg.br" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Phase transitions ; general studies ; Classical spin models ; Monte Carlo methods
• 刊名：Computer Physics Communications
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：209
• 期：Complete
• 页码：88-91
• 全文大小：571 K

文摘

Using the two dimensional class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516302466&_mathId=si21.gif&_user=111111111&_pii=S0010465516302466&_rdoc=1&_issn=00104655&md5=97d2d921aa87899d9397c8c0dd64ac03" title="Click to view the MathML source">XY−(S(O(3)))class="mathContainer hidden">class="mathCode">$XY-\left(S\left(O\left(3\right)\right)\right)$ model as a test case, we show that analysis of the Fisher zeros of the canonical partition function can provide signatures of a transition in the Berezinskii–Kosterlitz–Thouless (class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516302466&_mathId=si15.gif&_user=111111111&_pii=S0010465516302466&_rdoc=1&_issn=00104655&md5=528a59ea29569064b62ec6fa80a16516" title="Click to view the MathML source">BKTclass="mathContainer hidden">class="mathCode">$BKT$) universality class. Studying the internal border of zeros in the complex temperature plane, we found a scenario in complete agreement with theoretical expectations which allow one to uniquely classify a phase transition as in the class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516302466&_mathId=si15.gif&_user=111111111&_pii=S0010465516302466&_rdoc=1&_issn=00104655&md5=528a59ea29569064b62ec6fa80a16516" title="Click to view the MathML source">BKTclass="mathContainer hidden">class="mathCode">$BKT$ class of universality. We obtain class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516302466&_mathId=si24.gif&_user=111111111&_pii=S0010465516302466&_rdoc=1&_issn=00104655&md5=d5fa4742ea17b9088874cd3da27a2019">class="imgLazyJSB inlineImage" height="14" width="27" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0010465516302466-si24.gif">class="mathContainer hidden">class="mathCode">$T_{\mathrm{BKT}}$ in excellent accordance with previous results. A careful analysis of the behavior of the zeros for both regions class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516302466&_mathId=si25.gif&_user=111111111&_pii=S0010465516302466&_rdoc=1&_issn=00104655&md5=e6b238b9a87d8b5d0bab883a51203f0f">class="imgLazyJSB inlineImage" height="15" width="89" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0010465516302466-si25.gif">class="mathContainer hidden">class="mathCode">$\mathfrak{R}\mathfrak{e}\left(T\right)\le T_{\mathrm{BKT}}$ and class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516302466&_mathId=si26.gif&_user=111111111&_pii=S0010465516302466&_rdoc=1&_issn=00104655&md5=f65a597fd24728c078eafd334063e461">class="imgLazyJSB inlineImage" height="15" width="89" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0010465516302466-si26.gif">class="mathContainer hidden">class="mathCode">$\mathfrak{R}\mathfrak{e}\left(T\right)>T_{\mathrm{BKT}}$ in the thermodynamic limit shows that class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465516302466&_mathId=si27.gif&_user=111111111&_pii=S0010465516302466&_rdoc=1&_issn=00104655&md5=1b3e57e456bbac6307e520921f02ccbb" title="Click to view the MathML source">Im(T)class="mathContainer hidden">class="mathCode">$\mathfrak{I}\mathfrak{m}\left(T\right)$ goes to zero in the former case and is finite in the last one.