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arXiv · 0901.1010

A new Kempe invariant and the (non)-ergodicity of the Wang-Swendsen-Kotecky algorithm

Bojan Mohar·Jesus Salas
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Abstract

We prove that for the class of three-colorable triangulations of a closed oriented surface, the degree of a four-coloring modulo 12 is an invariant under Kempe changes. We use this general result to prove that for all triangulations T(3L,3M) of the torus with 3<= L <= M, there are at least two Kempe equivalence classes. This result implies in particular that the Wang-Swendsen-Kotecky algorithm for the zero-temperature 4-state Potts antiferromagnet on these triangulations T(3L,3M) of the torus is not ergodic.

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Bojan Mohar, Jesus Salas. 2009-05-22. A new Kempe invariant and the (non)-ergodicity of the Wang-Swendsen-Kotecky algorithm. https://doi.org/10.1088/1751-8113%2F42%2F22%2F225204

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