Four-point interfacial correlation functions in two dimensions. Exact results from field theory and numerical simulations

TL;DR

This paper derives exact four-point correlation functions for 2D phase-separating models, specifically applying to the Ising model, and confirms results with high-precision simulations.

Contribution

It provides the first exact analytic expressions for four-point interfacial correlations in 2D statistical models and validates them through numerical simulations.

Findings

Exact analytic formulas for four-point functions

Excellent agreement with Monte Carlo simulations

Advances understanding of interfacial correlations in 2D

Abstract

We derive exact analytic results for several four-point correlation functions for statistical models exhibiting phase separation in two-dimensions. Our theoretical results are then specialized to the Ising model on the two-dimensional strip and found to be in excellent agreement with high-precision Monte Carlo simulations.