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

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

2009-01-08

arxiv.org/abs/0901.1010v2

J. Phys. A: Math. Theor. 42 (2009) 225204

Mathematics

Combinatorics

37 pages (LaTeX2e). Includes tex file and 3 additional style files. The tex file includes 14 figures using pstricks.sty. Minor

Scientific paper

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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