关于晶格气体与反铁磁Potts模型的未解决问题清单
统计力学
2007-05-23 v3 数学物理
组合数学
math.MP
概率论
摘要
我回顾了关于硬核晶格气体和q着色模型（零温反铁磁Potts模型）的近期结果与未解决问题。对每个模型，我考虑了其平衡性质（无限体积吉布斯测度的唯一性/非唯一性、配分函数的复零点）以及局部和非局部蒙特卡洛算法的动力学（遍历性、快速混合、复逸度下的混合）。这些问题涉及数学物理、概率论、组合学和理论计算机科学。
引用
@article{arxiv.cond-mat/0004231,
title = {A Personal List of Unsolved Problems Concerning Lattice Gases and Antiferromagnetic Potts Models},
author = {Alan D. Sokal},
journal= {arXiv preprint arXiv:cond-mat/0004231},
year = {2007}
}
备注
19 pages, LaTeX2e. Talk presented at the conference on Inhomogeneous Random Systems, Universit\'e de Cergy-Pontoise, 25 January 2000. To appear in Markov Processes and Related Fields. Version 2 corrects some mistakes in Sections 4 and 5 (confusion between different notions of mixing time). Version 3 makes the title more specific, adds discussion of the disagreement-percolation method, and makes a few other small improvements