### Abstract

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+bβ^{e-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.

Original language | English (US) |
---|---|

Pages (from-to) | 25-47 |

Number of pages | 23 |

Journal | Journal of Statistical Physics |

Volume | 105 |

Issue number | 1-2 |

DOIs | |

State | Published - Oct 2001 |

### Fingerprint

### Keywords

- Antiferromagnetic Potts model
- Corrections to scaling
- Height representation
- Renormalization group
- Six-vertex model

### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics

### Cite this

*Journal of Statistical Physics*,

*105*(1-2), 25-47. https://doi.org/10.1023/A:1012273825098

**Unusual corrections to scaling in the 3-state Potts antiferromagnet on a square lattice.** / Cardy, John; Jacobsen, Jesper Lykke; Sokal, Alan D.

Research output: Contribution to journal › Article

*Journal of Statistical Physics*, vol. 105, no. 1-2, pp. 25-47. https://doi.org/10.1023/A:1012273825098

}

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.

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

UR - http://www.scopus.com/inward/record.url?scp=0035486418&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035486418&partnerID=8YFLogxK

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 -