论文标题
Wang-Swendsen的奇异性 - kotecký算法在圆环上的几类晶格上
Ergodicity of the Wang--Swendsen--Kotecký algorithm on several classes of lattices on the torus
论文作者
论文摘要
我们证明了Wang-swendsen-kotecký（WSK）算法在零温度上的零温度$ q $ -State Potts Anteromagnet上的算法。特别是，WSK算法对于$ q \ ge 4 $的巨像是围绕着围栏的任何四个$ \ ge 4 $。 It is also ergodic for $q \ge 5$ (resp. $q \ge 3$) on any Eulerian triangulation of the torus such that one sublattice consists of degree-4 vertices while the other two sublattices induce a quadrangulation of girth $\ge 4$ (resp.~a bipartite quadrangulation) of the torus.这些类别包括许多对统计力学感兴趣的晶格。
We prove the ergodicity of the Wang--Swendsen--Kotecký (WSK) algorithm for the zero-temperature $q$-state Potts antiferromagnet on several classes of lattices on the torus. In particular, the WSK algorithm is ergodic for $q\ge 4$ on any quadrangulation of the torus of girth $\ge 4$. It is also ergodic for $q \ge 5$ (resp. $q \ge 3$) on any Eulerian triangulation of the torus such that one sublattice consists of degree-4 vertices while the other two sublattices induce a quadrangulation of girth $\ge 4$ (resp.~a bipartite quadrangulation) of the torus. These classes include many lattices of interest in statistical mechanics.
