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

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.

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