作者：
Salas, JesusSokal, Alan D.Univ Carlos III Madrid
Dept Matemat Avda Univ 30 Leganes 28911 Spain Univ Carlos III Madrid
Unidad Asociada Inst Estruct Mat CSIC Grp Teorias Campos & Fis EstadistInst Gregorio M Madrid Spain UCL
Dept Math Gower St London WC1E 6BT England NYU
Dept Phys 726 Broadway New York NY 10003 USA
We prove the ergodicity of the wang-swendsen-kotecky (WSK) algorithm for the zero-temperature q-state Potts anti ferromagnet on several classes of lattices on the torus. In particular, the WSK algorithm is ergodic for...
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We prove the ergodicity of the wang-swendsen-kotecky (WSK) algorithm for the zero-temperature q-state Potts anti ferromagnet 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.
作者：
Salas, JSokal, ADUniv Zaragoza
Fac Ciencias Dept Fis Mat Condensada E-50009 Zaragoza Spain Univ Zaragoza
Fac Ciencias Dept Fis Teor E-50009 Zaragoza Spain NYU
Dept Phys New York NY 10003 USA
We study the 3-state square-lattice Potts antiferromagnet at zero temperature by a Monte Carlo simulation using the wang-swendsen-kotecky cluster algorithm, on lattices up to 1024 x 1024. We confirm the critical expon...
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We study the 3-state square-lattice Potts antiferromagnet at zero temperature by a Monte Carlo simulation using the wang-swendsen-kotecky cluster algorithm, on lattices up to 1024 x 1024. We confirm the critical exponents predicted by Burton and Henley based on the height representation of this model.
Let G be a graph with a vertex colouring alpha. Let a and b be two colours. Then a connected component of the subgraph induced by those vertices coloured either a or b is known as a Kempe chain. A colouring of G obtai...
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Let G be a graph with a vertex colouring alpha. Let a and b be two colours. Then a connected component of the subgraph induced by those vertices coloured either a or b is known as a Kempe chain. A colouring of G obtained from alpha by swapping the colours on the vertices of a Kempe chain is said to have been obtained by a Kempe change. Two colourings of G are Kempe equivalent if one can be obtained from the other by a sequence of Kempe changes. A conjecture of Mohar (2007) asserts that, for k >= 3, all k-colourings of a k-regular graph that is not complete are Kempe equivalent. It was later shown that all 3-colourings of a cubic graph that is neither K-4 nor the triangular prism are Kempe equivalent. In this paper, we prove that the conjecture holds for each k >= 4. We also report the implications of this result on the validity of the wang-swendsen-kotecky algorithm for the antiferromagnetic Potts model at zero-temperature. (C) 2018 Elsevier Inc. All rights reserved.
study the antiferromagnetic q-state Potts model on the square lattice for q = 3 and q = 4, using the wang-swendsen-kotecky (WSK) Monte Carlo algorithm and a powerful finite-size-scaling extrapolation method. For q=3 w...
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study the antiferromagnetic q-state Potts model on the square lattice for q = 3 and q = 4, using the wang-swendsen-kotecky (WSK) Monte Carlo algorithm and a powerful finite-size-scaling extrapolation method. For q=3 we obtain good control up to correlation length xi similar to 5000;the data are consistent with xi(B)=Ae(2 beta)beta(P)(1 + a(1)e(-beta) + ...) as beta--> infinity, with p approximate to 1. The staggered susceptibility behaves as chi(stagg) similar to xi(5/3). For q = 4 the model is disordered (xi less than or similar to 2) even at zero temperature. In appendices we prove a correlation inequality for Potts antiferromagnets on a bipartite lattice, and we prove ergodicity of the WSK algorithm at zero temperature for Potts antiferromagnets on a bipartite lattice.
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