Critical curves in conformally invariant statistical systems

TL;DR

This paper links conformally invariant critical curves in 2D statistical systems with Coulomb gas CFT and SLE, enabling the calculation of fractal properties and multifractal spectra of these curves.

Contribution

It establishes a formal connection between Coulomb gas CFT descriptions and SLE for critical curves, facilitating analysis of their fractal characteristics.

Findings

Derived the relation between Coulomb gas formalism and SLE for critical curves.

Provided methods to compute multifractal spectra of harmonic measure.

Linked conformal invariance with stochastic Loewner evolution in critical phenomena.

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.