Antiferromagnetic Potts Models on the Square Lattice: A High-Precision Monte Carlo Study
نویسندگان
چکیده
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) = Ae2ββp(1 + a1e −β + . . .) as β → ∞, with p ≈ 1. The staggered susceptibility behaves as χstagg ∼ ξ5/3. 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.
منابع مشابه
Antiferromagnetic Potts models on the square lattice.
We study the antiferromagnetic q-state Potts model on the square lattice for q = 3 and q = 4, using the Wang-Swendsen-Koteck y Monte Carlo algorithm and a new nite-size-scaling extrapolation method. For q = 3 we obtain good control up to correlation length 5000; the data are consistent with () = Ae 2 (1 + a 1 e +. . .) as ! 1. For q = 4 the model is disordered even at zero temperature.
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