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

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

2010-08-06

arxiv.org/abs/1008.1216v1

Physics

Condensed Matter

Statistical Mechanics

5 pages, 3 figures, 1 table

Scientific paper

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

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