Thomas Creighton K, Middleton A Alan
Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208-3108, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Apr;87(4):043303. doi: 10.1103/PhysRevE.87.043303. Epub 2013 Apr 5.
A powerful existing technique for evaluating statistical mechanical quantities in two-dimensional Ising models is based on constructing a matrix representing the nearest-neighbor spin couplings and then evaluating the Pfaffian of the matrix. Utilizing this technique and other more recent developments in evaluating elements of inverse matrices and exact sampling, a method and computer code for studying two-dimensional Ising models is developed. The formulation of this method is convenient and fast for computing the partition function and spin correlations. It is also useful for exact sampling, where configurations are directly generated with probability given by the Boltzmann distribution. These methods apply to Ising model samples with arbitrary nearest-neighbor couplings and can also be applied to general dimer models. Example results of computations are described, including comparisons with analytic results for the ferromagnetic Ising model, and timing information is provided.
一种用于评估二维伊辛模型中统计力学量的强大现有技术是基于构建一个表示最近邻自旋耦合的矩阵，然后计算该矩阵的Pfaffian。利用该技术以及在评估逆矩阵元素和精确采样方面的其他最新进展，开发了一种用于研究二维伊辛模型的方法和计算机代码。该方法的公式化对于计算配分函数和自旋相关性既方便又快速。它对于精确采样也很有用，在精确采样中，构型是根据玻尔兹曼分布给出的概率直接生成的。这些方法适用于具有任意最近邻耦合的伊辛模型样本，也可应用于一般的二聚体模型。文中描述了计算的示例结果，包括与铁磁伊辛模型解析结果的比较，并提供了计时信息。
