Antiferromagnetic Potts Models on the Square Lattice: A High-Precision Monte Carlo Study |
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Authors: | Ferreira Sabino José Sokal Alan D |
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Institution: | (1) Departamento de Estatística—ICEx, Universidade Federal de Minas Gerais, Belo Horizonte, MG 30161-970, Brazil;(2) Department of Physics, New York University, New York, s[New York, 10003 |
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Abstract: | We study the antiferromagnetic q-state Potts model on the square lattice for q=3 and q=4, using the Wang–Swendsen–Kotecký (WSK) Monte Carlo algorithm and a powerful finite-size-scaling extrapolation method. For q=3 we obtain good control up to correlation length ![xgr](/content/v516705398g14144/xxlarge958.gif) 5000; the data are consistent with ( )=Ae
2
p
(1+a
1
e
–
+ ...) as ![beta](/content/v516705398g14144/xxlarge946.gif) ![rarr](/content/v516705398g14144/xxlarge8594.gif) , with p 1. The staggered susceptibility behaves as
stagg![sim](/content/v516705398g14144/xxlarge8764.gif)
5/3. For q=4 the model is disordered (![xgr](/content/v516705398g14144/xxlarge958.gif) 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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Keywords: | Potts model antiferromagnet square lattice phase transition zero-temperature critical point Monte Carlo cluster algorithm Swendsen– Wang algorithm Wang– Swendsen– Kotecký algorithm finite-size scaling |
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