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Ergodicity of the Wang-Swendsen-Kotecký algorithm on several classes of lattices on the torus

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URI: https://hdl.handle.net/10016/35976
DOI: 10.1088/1751-8121/ac92ae
UXXI: AR/0000031305
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Ergodicity_Salas_JOPAMAT_2022_ps.pdf (579.92 KB)
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2022-10-05
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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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Eulerian triangulations, Quadrangulations, Torus, Kempe chains, Antiferromagnetic potts model, Wang-Swendsen-Kotecký algorithm, Ergodicity
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Salas, J. & Sokal, A. D. (2022). Ergodicity of the Wang–Swendsen–Kotecký algorithm on several classes of lattices on the torus. Journal of Physics A: Mathematical and Theoretical, 55(41), 415004.
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