TY - JOUR

T1 - Unusual corrections to scaling in the 3-state Potts antiferromagnet on a square lattice

AU - Cardy, John

AU - Jacobsen, Jesper Lykke

AU - Sokal, Alan D.

N1 - Funding Information:
This research was supported in part by EPSRC grant GR/J 78327 (J.L.C.) and NSF grant PHY–9900769 (A.D.S.). It was begun while A.D.S. was a Visiting Fellow at All Souls College, Oxford, where his work was supported in part by EPSRC grant GR/M 71626 and aided by the warm hospitality of the Department of Theoretical Physics. It was continued while J.L.J. and J.L.C. were hosted by the Centre de Recherches

PY - 2001/10

Y1 - 2001/10

N2 - At zero temperature, the 3-state antiferromagnetic Potts model on a square lattice maps exactly onto a point of the 6-vertex model whose long-distance behavior is equivalent to that of a free scalar boson. We point out that at nonzero temperature there are two distinct types of excitation: vortices, which are relevant with renormalization-group eigenvalue 1/2; and non-vortex unsatisfied bonds, which are strictly marginal and serve only to renormalize the stiffness coefficient of the underlying free boson. Together these excitations lead to an unusual form for the corrections to scaling: for example, the correlation length diverges as β ≡ J / kT → ∞ according to ξ ∼ Ae2β(1+bβe-β+⋯), where b is a nonuniversal constant that may nevertheless be determined independently. A similar result holds for the staggered susceptibility. These results are shown to be consistent with the anomalous behavior found in the Monte Carlo simulations of Ferreira and Sokal.

AB - At zero temperature, the 3-state antiferromagnetic Potts model on a square lattice maps exactly onto a point of the 6-vertex model whose long-distance behavior is equivalent to that of a free scalar boson. We point out that at nonzero temperature there are two distinct types of excitation: vortices, which are relevant with renormalization-group eigenvalue 1/2; and non-vortex unsatisfied bonds, which are strictly marginal and serve only to renormalize the stiffness coefficient of the underlying free boson. Together these excitations lead to an unusual form for the corrections to scaling: for example, the correlation length diverges as β ≡ J / kT → ∞ according to ξ ∼ Ae2β(1+bβe-β+⋯), where b is a nonuniversal constant that may nevertheless be determined independently. A similar result holds for the staggered susceptibility. These results are shown to be consistent with the anomalous behavior found in the Monte Carlo simulations of Ferreira and Sokal.

KW - Antiferromagnetic Potts model

KW - Corrections to scaling

KW - Height representation

KW - Renormalization group

KW - Six-vertex model

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U2 - 10.1023/A:1012273825098

DO - 10.1023/A:1012273825098

M3 - Article

AN - SCOPUS:0035486418

VL - 105

SP - 25

EP - 47

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 1-2

ER -