热力学极限下Yang-Lee零点密度的张量网络方法
Density of Yang-Lee zeros in the thermodynamic limit from tensor network methods
摘要：
利用张量网络方法，直接在热力学极限下，研究了二维和三维铁磁伊辛模型的Yang-Lee零点在复场平面上的分布.的配分函数表示为一个张量网络的收缩，并有效地评估与迭代张量重整化方案。在复场平面上计算了自由能量密度和磁化强度。通过磁化强度的不连续性，得到了单位圆上的Yang-Lee零点密度，与Lee-Yang圆定理一致。在低于、高于和处于临界温度的不同温度下观察到不同的特征。张量网络方法的应用也$q$状态Potts模型在两个和三个维度和以前的辩论是否，在热力学极限，杨-李零点躺在单位圆$q>2$是解决：他们显然不躺在单位圆，除了在零温度。对于二维Potts模型（q= 3，4，5，6），随着温度的降低，与实轴成固定角度的零点半径随着温度的倒数指数地向1方向收缩。
英文摘要：
The distribution of Yang-Lee zeros in the ferromagnetic Ising model in both two and three dimensions is studied on the complex field plane directly in the thermodynamic limit via the tensor network methods. The partition function is represented as a contraction of a tensor network and is efficiently evaluated with an iterative tensor renormalization scheme. The free-energy density and the magnetization are computed on the complex field plane. Via the discontinuity of the magnetization, the density of the Yang-Lee zeros is obtained to lie on the unit circle, consistent with the Lee-Yang circle theorem. Distinct features are observed at different temperatures---below, above and at the critical temperature. Application of the tensor-network approach is also made to the $q$-state Potts models in both two and three dimensions and a previous debate on whether, in the thermodynamic limit, the Yang-Lee zeros lie on a unit circle for $q>2$ is resolved: they clearly do not lie on a unit circle except at the zero temperature. For the Potts models (q=3,4,5,6) investigated in two dimensions, as the temperature is lowered the radius of the zeros at a fixed angle from the real axis shrinks exponentially towards unity with the inverse temperature.
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