Critical curves in conformally invariant statistical systems

Details Critical curves in conformally invariant statistical systems Critical curves in conformally invariant statistical systems

2006-10-19

arxiv.org/abs/cond-mat/0610550v2

J. Phys. A: Math. Theor. 40 (2007)

Physics

Condensed Matter

Statistical Mechanics

Published version

Scientific paper

10.1088/1751-8113/40/9/020

We consider critical curves -- conformally invariant curves that appear at critical points of two-dimensional statistical mechanical systems. We show how to describe these curves in terms of the Coulomb gas formalism of conformal field theory (CFT). We also provide links between this description and the stochastic (Schramm-) Loewner evolution (SLE). The connection appears in the long-time limit of stochastic evolution of various SLE observables related to CFT primary fields. We show how the multifractal spectrum of harmonic measure and other fractal characteristics of critical curves can be obtained.

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