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

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_{l_1-l_2,2 l_1}, valid for 0 </- Q </- 4, that describe the insertion of l_1 thin and l_2 thick domain walls.

5 pages, 3 figures, 1 table

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• 2D growth processes: SLE and Loewner chains
• Topological order from quantum loops and nets
• SLE in the three-state Potts model - a numerical study
• Loop models and their critical points

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