The partition function of gauge supersymmetric Ising model on 3D regular lattice

Partition function zeros and leading order scaling correction of the 3D Ising model from multicanonical simulations

The density of states for the three-dimensional Ising model is calculated with high-precision from multicanonical simulations. This allows us to estimate the leading partition function zeros for lattice sizes up to L=32. Combining previous statistics for smaller lattice sizes, we have evaluated the correction to scaling and the critical exponent $ν$ through out an analysis of a multi-parameter fit and of Bulirsch-Stoer (BST) extrapolation algorithm. The performance of the BST algorithm is also explored in case of the 2D Ising model, where the exact partition function zeros are known.

高自旋二维伊辛模型的配分函数零点

Zeros of the Partition Function for Higher--Spin 2D Ising Models

本文计算了自旋为$s=1$、3/2和2的正方晶格上二维伊辛模型的配分函数的复温度零点。这些给洞察这些模型在热力学极限的复杂的温度相图。支持举出的猜想，所有的分歧的磁化强度发生在端点的弧的零突出到FM相位。我们猜想对于$s \ge 1$存在这样的弧$4[s^2]-2$，其中$[x]$表示$x$的整数部分。

Potts模型的系列研究。第一章简单立方伊辛模型

Series studies of the Potts model. I: The simple cubic Ising model

本文将有限格点级数展开法推广到简单立方格点上的$q$态Potts模型。据发现，计算工作量的增长指数与平方的数量的系列条款获得，不像二维晶格的计算需求增长指数与条款的数量。对于伊辛（$q=2$）的情况下，我们已经扩展了低温系列的配分函数，磁化强度和零场磁化率$u^{26}$从$u^{20}$。将零场配分函数的高温级数从$v^{18}$推广到$v^{22}$。随后的分析给出了与场论一致的临界指数。

Ising自旋玻璃的配分函数零点

Partition Function Zeros of an Ising Spin Glass

我们研究了在不同尺寸的常规有限晶格上，伊辛自旋玻璃的精确配分函数计算所产生的零点模式。大量的随机键的配置探测淬火平均的框架。本研究的动机是层次晶格模型的配分函数零点落在Julia集和混沌重整化流在这样的模型与挫折之间的关系，并通过可能的连接，后者与自旋玻璃行为。在任何有限体积中，所有配分函数的零点的同时分布可以被看作是寻找某类具有正整数系数的随机多项式的所有零点的位置的更一般问题的一部分。这个问题的一些方面已经在数学的各个分支进行了研究，我们将展示如何多项式映射，用于图论中的分类图，可能有助于在零的分布特性。最后，我们讨论了可能的极限集的体积发送到无穷大。

Singularities of the Partition Function for the Ising Model Coupled to 2d Quantum Gravity

We study the zeros in the complex plane of the partition function for the Ising model coupled to 2d quantum gravity for complex magnetic field and real temperature, and for complex temperature and real magnetic field, respectively. We compute the zeros by using the exact solution coming from a two matrix model and by Monte Carlo simulations of Ising spins on dynamical triangulations. We present evidence that the zeros form simple one-dimensional curves in the complex plane, and that the critical behaviour of the system is governed by the scaling of the distribution of the singularities near th…

Vortex characterisation of frustration in the 2d Ising spin glass

The frustrated Ising model on a two-dimensional lattice with open boundary conditions is revisited. A hidden Z2 gauge symmetry relates models with different frustrations which, however, share the same partition function. By means of a duality transformation, it is shown that the partition function only depends on the distribution of gauge invariant vortices on the lattice. We finally show that the exact ground state energy can be calculated in polynomial time using Edmonds' algorithm.