Schramm-Loewner evolution theory of the asymptotic behaviors of -dimensional Wolf-Villain model

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• 作者：Yili Chen ^{chenyili@cumt.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Gang Tang ; ^{gangtang@cumt.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Zhipeng Xun ; Lei Zhu ; Zhe Zhang
• 关键词：Wolf&ndash ; Villain model ; Schramm&ndash ; Loewner evolution ; Edward&ndash ; Wilkinson universality class
• 刊名：Physica A: Statistical Mechanics and its Applications
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：465
• 期：Complete
• 页码：613-620
• 全文大小：1268 K

文摘

Although extensive analytical and numerical work has focus on investigating the (2+1)-dimensional Wolf–Villain (WV) model, some problems concerning its asymptotical behaviors, such as the universality class to which it belongs remain controversial. The Schramm–Loewner evolution (SLE) theory is an attractive approach to describe the fluctuation phenomena and random processes, and has also been applied to the analysis of the stochastic growth of surfaces. In this work, we applied SLE theory to the analysis of the saturated surface to conduct in-depth research, with a new perspective, on the asymptotical behaviors of the (2+1)-dimensional WV model. On the basis of the analysis of the saturated surface contour lines, we determine that the diffusion coefficient calculated for (2+1)-dimensional WV model is class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S037843711630574X&_mathId=si8.gif&_user=111111111&_pii=S037843711630574X&_rdoc=1&_issn=03784371&md5=9c515d568d6baebab7ca2c8c44a11bc6" title="Click to view the MathML source">κ=2.91±0.01class="mathContainer hidden">class="mathCode">$\kappa =2.91\pm 0.01$, and that for Family model is class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S037843711630574X&_mathId=si9.gif&_user=111111111&_pii=S037843711630574X&_rdoc=1&_issn=03784371&md5=0e0fb27c75f7268b4a7e89a133038675" title="Click to view the MathML source">κ=2.88±0.01class="mathContainer hidden">class="mathCode">$\kappa =2.88\pm 0.01$. Accordingly we can conclude from the view of SLE theory, that the (2+1)-dimensional WV model, similar to the Family model, also belongs to the Edwards–Wilkinson universality class.