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

István A. Kovács; Jean Christian Anglès D'Auriac; Ferenc Iglói

doi: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

István A. Kovács^*, Jean Christian Anglès D'Auriac, Ferenc Iglói

^*Corresponding author for this work

Physics and Astronomy

Research output: Contribution to journal › Article › peer-review

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_Γis 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 (US)
Article number	P09019
Journal	Journal of Statistical Mechanics: Theory and Experiment
Volume	2014
Issue number	9
DOIs	https://doi.org/10.1088/1742-5468/2014/09/P09019
State	Published - Sep 1 2014

Keywords

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

ASJC Scopus subject areas

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

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abstract = "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.",

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AU - Iglói, Ferenc

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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.

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