Critical curves in conformally invariant statistical systems

Abstract

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.

Published version

References in corpus (2)

• A Guide to Stochastic Loewner Evolution and its Applications
• Stochastic Loewner evolution for conformal field theories with Lie-group symmetries

Cited by in corpus (4)

• Global properties of Stochastic Loewner evolution driven by Levy processes
• Harmonic measure and winding of random conformal paths: A Coulomb gas perspective
• Statistics of harmonic measure and winding of critical curves from conformal field theory
• Disordered O(n) Loop Model and Coupled Conformal Field Theories