Multipoint correlation functions at phase separation. Exact results from field theory

TL;DR

This paper derives exact formulas for multipoint correlation functions in near-critical two-dimensional systems with phase separation, revealing detailed interfacial fluctuation behavior using field theory techniques.

Contribution

It introduces a novel method to compute arbitrary multipoint correlations in boundary-induced phase separation, providing explicit formulas and insights into interfacial fluctuations.

Findings

Explicit three-point correlation function derived

Long-range interfacial fluctuation behavior characterized

Finite-size effects and mixed correlations analyzed

Abstract

We consider near-critical two-dimensional statistical systems with boundary conditions inducing phase separation on the strip. By exploiting low-energy properties of two-dimensional field theories, we compute arbitrary $n$-point correlation of the order parameter field. Finite-size corrections and mixed correlations involving the stress tensor trace are also discussed. As an explicit illustration of the technique, we provide a closed-form expression for a three-point correlation function and illustrate the explicit form of the long-ranged interfacial fluctuations as well as their confinement within the interfacial region.