### Abstract

We consider the random-bond Potts model in the large-Q limit and calculate the excess entropy, S_{Γ}, of a contour, Γ, which is given by the mean number of Fortuin-Kasteleyn clusters which are crossed by Γ. In two dimensions, S_{Γ}is proportional to the length of Γ, to which-at the critical point-there are universal logarithmic corrections due to corners. These are calculated by applying techniques of conformal field theory and compared with the results of large scale numerical calculations. The central charge of the model is obtained from the corner contributions to the excess entropy and independently from the finite-size correction of the free-energy as: lim_{Q → ∞}c(Q)/lnQ = 0.74(2), close to previous estimates calculated at finite values of Q.

Original language | English |
---|---|

Article number | P09019 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Volume | 2014 |

Issue number | 9 |

DOIs | |

Publication status | Published - Sep 1 2014 |

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### Keywords

- classical phase transitions (theory)
- conformal field theory
- disordered systems (theory)
- finite-size scaling

### ASJC Scopus subject areas

- Statistics and Probability
- Statistical and Nonlinear Physics
- Statistics, Probability and Uncertainty

### Cite this

*Journal of Statistical Mechanics: Theory and Experiment*,

*2014*(9), [P09019]. https://doi.org/10.1088/1742-5468/2014/09/P09019

**Excess entropy and central charge of the two-dimensional random-bond Potts model in the large-Q limit.** / Kovács, István A.; Anglès D'Auriac, Jean Christian; Iglói, F.

Research output: Contribution to journal › Article

*Journal of Statistical Mechanics: Theory and Experiment*, vol. 2014, no. 9, P09019. https://doi.org/10.1088/1742-5468/2014/09/P09019

}

TY - JOUR

T1 - Excess entropy and central charge of the two-dimensional random-bond Potts model in the large-Q limit

AU - Kovács, István A.

AU - Anglès D'Auriac, Jean Christian

AU - Iglói, F.

PY - 2014/9/1

Y1 - 2014/9/1

N2 - We consider the random-bond Potts model in the large-Q limit and calculate the excess entropy, SΓ, of a contour, Γ, which is given by the mean number of Fortuin-Kasteleyn clusters which are crossed by Γ. In two dimensions, SΓis proportional to the length of Γ, to which-at the critical point-there are universal logarithmic corrections due to corners. These are calculated by applying techniques of conformal field theory and compared with the results of large scale numerical calculations. The central charge of the model is obtained from the corner contributions to the excess entropy and independently from the finite-size correction of the free-energy as: limQ → ∞c(Q)/lnQ = 0.74(2), close to previous estimates calculated at finite values of Q.

AB - We consider the random-bond Potts model in the large-Q limit and calculate the excess entropy, SΓ, of a contour, Γ, which is given by the mean number of Fortuin-Kasteleyn clusters which are crossed by Γ. In two dimensions, SΓis proportional to the length of Γ, to which-at the critical point-there are universal logarithmic corrections due to corners. These are calculated by applying techniques of conformal field theory and compared with the results of large scale numerical calculations. The central charge of the model is obtained from the corner contributions to the excess entropy and independently from the finite-size correction of the free-energy as: limQ → ∞c(Q)/lnQ = 0.74(2), close to previous estimates calculated at finite values of Q.

KW - classical phase transitions (theory)

KW - conformal field theory

KW - disordered systems (theory)

KW - finite-size scaling

UR - http://www.scopus.com/inward/record.url?scp=84907485832&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84907485832&partnerID=8YFLogxK

U2 - 10.1088/1742-5468/2014/09/P09019

DO - 10.1088/1742-5468/2014/09/P09019

M3 - Article

AN - SCOPUS:84907485832

VL - 2014

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

SN - 1742-5468

IS - 9

M1 - P09019

ER -