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Antiferromagnetic Potts Models on the Square Lattice: A High-Precision Monte Carlo Study

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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 ξ∼5000; the data are consistent with ξ(β)=Ae 2β β p(1+a 1 e −β+ ...) as β→∞, with p≈1. The staggered susceptibility behaves as χ stagg∼ξ 5/3. For q=4 the model is disordered (ξ≲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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  1. Departamento de Estatística—ICEx, Universidade Federal de Minas Gerais, Belo Horizonte, MG 30161-970, Brazil

    Sabino José Ferreira

  2. Department of Physics, New York University, New York, s[New York, 10003

    Alan D. Sokal

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Ferreira, S.J., Sokal, A.D. Antiferromagnetic Potts Models on the Square Lattice: A High-Precision Monte Carlo Study. Journal of Statistical Physics 96, 461–530 (1999). https://doi.org/10.1023/A:1004599121565

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