Location of zeros for the partition function of the Ising model on bounded degree graphs

Peters Han; Regts Guus

摘要

Abstract > The seminal Lee–Yang theorem states that for any graph the zeros of the partition function of the ferromagnetic Ising model lie on the unit circle in <mat:math display="inline" altimg="urn:x-wiley:00246107:media:jlms12286:jlms12286-math-0001" wiley:location="equation/jlms12286-math-0001.png"> <mat:mi mathvariant="double-struck">C</mat:mi> </mat:math> . In fact, the union of the zeros of all graphs is dense on the unit circle. In this paper, we study the location of the zeros for the class of graphs of bounded maximum degree <mat:math display="inline" altimg="urn:x-wiley:00246107:media:jlms12286:jlms12286-math-0002" wiley:location="equation/jlms12286-math-0002.png"> <mat:mrow> <mat:mi>d</mat:mi> <mat:mo>?</mat:mo> <mat:mn>3</mat:mn> </mat:mrow> </mat:math> , both in the ferromagnetic and the anti‐ferromagnetic case. We determine the location exactly as a function of the inverse temperature and the degree <mat:math display="inline" altimg="urn:x-wiley:00246107:media:jlms12286:jlms12286-math-0003" wiley:location="equation/jlms12286-math-0003.png"> <mat:mi>d</mat:mi> </mat:math> . An important step in our approach is to translate to the setting of complex dynamics and analyze a dynamical system that is naturally associated to the partition?function. </abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> <div class="translation abstracttxt"> <span class="zhankaihshouqi fivelineshidden" id="abstract"> <span>机译：</span><Abstract Type =“Main”XML：Lang =“en”> <标题类型=“main”>抽象</ title> > Omeminal Lee-yang定理说，对于任何曲线图，铁磁ising模型的分区功能的零位于单位圈 <mat：数学显示=“内联”Altimg =“URN：X-Wiley：00246107：媒体：JLMS12286：JLMS12286-Math-0001”Wiley：location =“等式/ jlms12286-math-0001.png”> <mat：mi mathvariant =“双击”> c </ mat：mi> </ mat：math> 。实际上，单位圈子上的所有图的零的结合是密集的。在本文中，我们研究了Zeros的位置，用于有界最大程度的阶级的图表 <mat：数学显示=“内联”Altimg =“URN：X-Wiley：00246107：媒体：JLMS12286：JLMS12286-Math-0002”Wiley：Location =“等式/ JLMS12286-Math-0002.png”> <MAT：MROW> <MAT：MI> D </ MAT：MI> <mat：mo>？</ mat：mo> <MAT：MN> 3 </ MAT：MN> </ mat：MROW> </ mat：math> ，无论是铁磁和抗铁磁盒。我们确定了与逆温和程度的函数的位置 <mat：数学显示=“内联”Altimg =“URN：X-Wiley：00246107：媒体：JLMS12286：JLMS12286-Math-0003”Wiley：Location =“等式/ JLMS12286-Math-0003.png”> <MAT：MI> D </ MAT：MI> </ mat：math> 。我们方法的一个重要步骤是转化为复杂动态的设置，并分析与分区自然相关的动态系统？功能。 </ p> </摘要> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> </div> <div class="record"> <h2 class="all_title" id="enpatent33" > 著录项</h2> <ul> <li> <span class="lefttit">来源</span> <div style="width: 86%;vertical-align: text-top;display: inline-block;"> <a href='/journal-foreign-31023/'>《The Journal of the London Mathematical Society 》</a> <b style="margin: 0 2px;">|</b><span>2020年第2期</span><b style="margin: 0 2px;">|</b> <span>共21页</span> </div> </li> <li> <div class="author"> <span class="lefttit">作者</span> <p id="fAuthorthree" class="threelineshidden zhankaihshouqi"> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Peters Han&option=202" target="_blank" rel="nofollow">Peters Han;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Regts Guus&option=202" target="_blank" rel="nofollow">Regts Guus;</a> </p> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zkzz" style="display: none;">展开▼</span> </div> </li> <li> <div style="display: flex;"> <span class="lefttit">作者单位</span> <div style="position: relative;margin-left: 3px;max-width: 639px;"> <div class="threelineshidden zhankaihshouqi" id="fOrgthree"> <p>Korteweg de Vries Institute for MathematicsUniversity of AmsterdamScience Park 107 1090GE Amsterdam the Netherlands;</p> <p>Korteweg de Vries Institute for MathematicsUniversity of AmsterdamScience Park 107 1090GE Amsterdam the Netherlands;</p> </div> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zhdw" style="display: none;">展开▼</span> </div> </div> </li> <li> <span class="lefttit">收录信息</span> <span style="width: 86%;vertical-align: text-top;display: inline-block;"></span> </li> <li> <span class="lefttit">原文格式</span> <span>PDF</span> </li> <li> <span class="lefttit">正文语种</span> <span>eng</span> </li> <li> <span class="lefttit">中图分类</span> <span> <a href="https://www.zhangqiaokeyan.com/clc/156.html" title="数学">数学 ;</a></span> </li> <li class="antistop"> <span class="lefttit">关键词</span> <p style="width: 86%;vertical-align: text-top;"> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=37F10&option=203" rel="nofollow">37F10;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=05C31&option=203" rel="nofollow">05C31;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=68W25&option=203" rel="nofollow">68W25;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=82B20 (primary)&option=203" rel="nofollow">82B20 (primary);</a> </p> <div class="translation"> 机译：37F10;05C31;68W25;82B20（主要）; 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