Corner contribution to cluster numbers in the Potts model

Istvan A. Kovacs; Eren Metin Elci; Martin Weigel; Ferenc Igloi

doi:10.1103/PhysRevB.89.064421

Corner contribution to cluster numbers in the Potts model

Istvan A. Kovacs, Eren Metin Elci, Martin Weigel, Ferenc Igloi

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Abstract

For the two-dimensional Q-state Potts model at criticality, we consider Fortuin-Kasteleyn and spin clusters and study the average number N of clusters that intersect a given contour . To leading order, N is proportional to the length of the curve. Additionally, however, there occur logarithmic contributions related to the corners of . These are found to be universal and their size can be calculated employing techniques from conformal field theory. For the Fortuin-Kasteleyn clusters relevant to the thermal phase transition, we find agreement with these predictions from large-scale numerical simulations. For the spin clusters, on the other hand, the cluster numbers are not found to be consistent with the values obtained by analytic continuation, as conventionally assumed.

Original language	English
Journal	Physical Review B
Volume	89
Issue number	Article 064421
DOIs	https://doi.org/10.1103/PhysRevB.89.064421
Publication status	Published - 24 Feb 2014

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Martin Weigel
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title = "Corner contribution to cluster numbers in the Potts model",

abstract = "For the two-dimensional Q-state Potts model at criticality, we consider Fortuin-Kasteleyn and spin clusters and study the average number N of clusters that intersect a given contour . To leading order, N is proportional to the length of the curve. Additionally, however, there occur logarithmic contributions related to the corners of . These are found to be universal and their size can be calculated employing techniques from conformal field theory. For the Fortuin-Kasteleyn clusters relevant to the thermal phase transition, we find agreement with these predictions from large-scale numerical simulations. For the spin clusters, on the other hand, the cluster numbers are not found to be consistent with the values obtained by analytic continuation, as conventionally assumed.",

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AU - Kovacs, Istvan A.

AU - Elci, Eren Metin

AU - Weigel, Martin

AU - Igloi, Ferenc

N1 - The publisher the American Physical Society gives permission for this article to be archived on the institutional repository

PY - 2014/2/24

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N2 - For the two-dimensional Q-state Potts model at criticality, we consider Fortuin-Kasteleyn and spin clusters and study the average number N of clusters that intersect a given contour . To leading order, N is proportional to the length of the curve. Additionally, however, there occur logarithmic contributions related to the corners of . These are found to be universal and their size can be calculated employing techniques from conformal field theory. For the Fortuin-Kasteleyn clusters relevant to the thermal phase transition, we find agreement with these predictions from large-scale numerical simulations. For the spin clusters, on the other hand, the cluster numbers are not found to be consistent with the values obtained by analytic continuation, as conventionally assumed.

AB - For the two-dimensional Q-state Potts model at criticality, we consider Fortuin-Kasteleyn and spin clusters and study the average number N of clusters that intersect a given contour . To leading order, N is proportional to the length of the curve. Additionally, however, there occur logarithmic contributions related to the corners of . These are found to be universal and their size can be calculated employing techniques from conformal field theory. For the Fortuin-Kasteleyn clusters relevant to the thermal phase transition, we find agreement with these predictions from large-scale numerical simulations. For the spin clusters, on the other hand, the cluster numbers are not found to be consistent with the values obtained by analytic continuation, as conventionally assumed.

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SN - 2469-9969

VL - 89

JO - Physical Review B

JF - Physical Review B

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Corner contribution to cluster numbers in the Potts model

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