Ergodicity of the Wang–Swendsen–Kotecký algorithm on several classes of lattices on the torus
Journal of Physics A(2022)
摘要
Abstract 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 ⩾ 4 on any quadrangulation of the torus of girth ⩾ 4 . It is also ergodic for q ⩾ 5 (resp. q ⩾ 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 ⩾ 4 (resp. a bipartite quadrangulation) of the torus. These classes include many lattices of interest in statistical mechanics.
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关键词
wang–swendsen–kotecký algorithm,lattices
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