Critical exponents of domain walls in the two-dimensional Potts model

2010/08/06 by Jérôme Dubail, Jesper Lykke Jacobsen, Hubert Saleur · 1 citation
Physics and Astronomy · #cond-mat.stat-mech

paper · pdf · doi:10.1088/1751-8113/43/48/482002

published as J. Phys. A: Math. Theor. 43 482002, 2010 · 5 pages, 3 figures, 1 table

arxiv created 2010/08/06 · arxiv updated 2017/12/22

Abstract

We address the geometrical critical behavior of the two-dimensional Q-state Potts model in terms of the spin clusters (i.e., connected domains where the spin takes a constant value). These clusters are different from the usual Fortuin-Kasteleyn clusters, and are separated by domain walls that can cross and branch. We develop a transfer matrix technique enabling the formulation and numerical study of spin clusters even when Q is not an integer. We further identify geometrically the crossing events which give rise to conformal correlation functions. This leads to an infinite series of fundamental critical exponents h_{l1-l2,2 l1}, valid for 0 </- Q </- 4, that describe the insertion of l₁ thin and l₂ thick domain walls.

Cited by

• Bulk and boundary critical behaviour of thin and thick domain walls in the two-dimensional Potts model

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