论文标题
第一个Lee-Yang零的热力学极限
Thermodynamic limit of the first Lee-Yang zero
论文作者
论文摘要
我们完成了1952年Yang和Lee提案的验证，即热力学奇异性正是$ {\ Mathbb c} $中有限量奇异性的$ {\ Mathbb r} $中的限制。对于在有限$λ\ subset \ mathbb {z}^d $下定义的ISING模型，在反温度$β\ geq0 $和外部字段$ h $时，让$α_1（λ，β）$是第一个零的模量（与其分区函数最接近）（在变量$ h $中）。 We prove that $α_1(Λ,β)$ decreases to $α_1(\mathbb{Z}^d,β)$ as $Λ$ increases to $\mathbb{Z}^d$ where $α_1(\mathbb{Z}^d,β)\in[0,\infty)$ is the radius of the largest disk centered at the origin in which热力学极限中的自由能是分析性的。我们还注意到，$α_1（\ mathbb {z}^d，β）$在且仅当$β$严格小于关键的逆温度时，才严格为正。
We complete the verification of the 1952 Yang and Lee proposal that thermodynamic singularities are exactly the limits in ${\mathbb R}$ of finite-volume singularities in ${\mathbb C}$. For the Ising model defined on a finite $Λ\subset\mathbb{Z}^d$ at inverse temperature $β\geq0$ and external field $h$, let $α_1(Λ,β)$ be the modulus of the first zero (that closest to the origin) of its partition function (in the variable $h$). We prove that $α_1(Λ,β)$ decreases to $α_1(\mathbb{Z}^d,β)$ as $Λ$ increases to $\mathbb{Z}^d$ where $α_1(\mathbb{Z}^d,β)\in[0,\infty)$ is the radius of the largest disk centered at the origin in which the free energy in the thermodynamic limit is analytic. We also note that $α_1(\mathbb{Z}^d,β)$ is strictly positive if and only if $β$ is strictly less than the critical inverse temperature.
