伊辛模型分层抽样的图论方法
Stratified Sampling for the Ising Model: A Graph-Theoretic Approach
摘要：
我们提出了一个新的方法来解决统计物理中的一个经典问题：铁磁伊辛模型的配分函数和其他热力学量的估计。马尔可夫链蒙特卡罗方法对这个问题已经得到了很好的研究，虽然一个算法，是真正实用的仍然难以捉摸。我们的方法利用了这样一个事实，即对于一个固定的键强度，研究铁磁伊辛模型是一个问题，一个给定的图计数特定的子图。我们结合图论和启发式采样，以确定系数是独立的温度，一旦获得，可用于确定的配分函数和计算物理量，如平均能量，平均磁矩，比热，和磁化率。
英文摘要：
We present a new approach to a classical problem in statistical physics: estimating the partition function and other thermodynamic quantities of the ferromagnetic Ising model. Markov chain Monte Carlo methods for this problem have been well-studied, although an algorithm that is truly practical remains elusive. Our approach takes advantage of the fact that, for a fixed bond strength, studying the ferromagnetic Ising model is a question of counting particular subgraphs of a given graph. We combine graph theory and heuristic sampling to determine coefficients that are independent of temperature and that, once obtained, can be used to determine the partition function and to compute physical quantities such as mean energy, mean magnetic moment, specific heat, and magnetic susceptibility.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
