Critical curves in conformally invariant statistical systems

E. Bettelheim; I. A. Gruzberg; I. Rushkin; P. Wiegmann

Critical curves in conformally invariant statistical systems

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arxiv cond-mat/0610550 v2 pith:URS5O7GO submitted 2006-10-19 cond-mat.stat-mech math-phmath.MPmath.PR

I. Rushkin , E. Bettelheim , I. A. Gruzberg , P. Wiegmann This is my paper · ORCID

classification cond-mat.stat-mechmath-phmath.MPmath.PR

keywords curvescriticalconformallyevolutioninvariantstatisticalstochasticsystems

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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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Fractal dimension of critical curves in the $O(n)$-symmetric $\phi^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models
cond-mat.stat-mech 2019-08 accept novelty 7.0 of 10

A six-loop field-theoretic calculation gives the fractal dimension of critical curves and the crossover exponent in O(n) models, with estimates for LERW, SAW, Ising, XY and Heisenberg systems.

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