A new Kempe invariant and the non-ergodicity of the Wang-Swendsen-Kotecky algorithm - Mathematics > CombinatoricsReport as inadecuate




A new Kempe invariant and the non-ergodicity of the Wang-Swendsen-Kotecky algorithm - Mathematics > Combinatorics - Download this document for free, or read online. Document in PDF available to download.

Abstract: We prove that for the class of three-colorable triangulations of a closedoriented surface, the degree of a four-coloring modulo 12 is an invariant underKempe changes. We use this general result to prove that for all triangulationsT3L,3M of the torus with 3<= L <= M, there are at least two Kempe equivalenceclasses. This result implies in particular that the Wang-Swendsen-Koteckyalgorithm for the zero-temperature 4-state Potts antiferromagnet on thesetriangulations T3L,3M of the torus is not ergodic.



Author: Bojan Mohar, Jesus Salas

Source: https://arxiv.org/







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