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arXiv:cond-mat/0201383

The ferro/antiferromagnetic q-state Potts model

Damien Paul Foster, C Gérard

Published Jan 22, 2002• 2 citations
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Abstract

The critical properties of the mixed ferro/antiferromagnetic q-state Potts model on the square lattice are investigated using the numerical transfer matrix technique. The transition temperature is found to be substantially lower than previously found for q=3. It is conjectured that there is no transition for q>3, in contradiction with previous results.

DOI
10.48550/arxiv.cond-mat/0201383

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The critical properties of the mixed ferro/antiferromagnetic q-state Potts model on the square lattice are investigated using the numerical transfer matrix technique. The transition temperature is found to be substantially lower than previously found for q=3. It is conjectured that there is no transition for q>3, in contradiction with previous results.
We study three-state Potts spins on a square lattice, in which all bonds are ferromagnetic along one of the lattice directions, and antiferromagnetic along the other. Numerical transfer-matrix methods are used on infinite strips of width L sites, 4 ⩽ L ⩽ 14. Based on the analysis of the ratio of scaled mass gaps (inverse correlation lengths) and scaled domain-wall free energies, we provide strong evidence that a critical (Kosterlitz–Thouless) phase is present, whose upper limit is, in our best estimate, T c = 0.29 ± 0.01. From an analysis of the (extremely anisotropic) nature of excitations below T c , we argue that the critical phase extends all the way down to T = 0. While domain walls parallel to the ferromagnetic direction are soft for the whole extent of the critical phase, those along the antiferromagnetic direction seem to undergo a softening transition at a finite temperature. Assuming a bulk correlation length varying, for T > T c , as ξ( T ) = a ξ exp[ b ξ ( T − T c ) −σ ], σ ≃ 1/2, we attempt finite-size scaling plots of our finite-width correlation lengths. Our best results are for T c = 0.50 ± 0.01. We propose a scenario in which such inconsistency is attributed to the extreme narrowness of the critical region.