Correlations and structure of interfaces in the Ising model. Theory and numerics

TL;DR

This paper combines field theory and Monte Carlo simulations to analyze phase separation and interface structures in the 2D Ising model near criticality, providing exact correlation functions and confirming them numerically.

Contribution

It offers exact analytic expressions for correlation functions and interface properties in the 2D Ising model, validated by numerical simulations.

Findings

Exact correlation functions derived analytically

Monte Carlo simulations confirm theoretical predictions

Detailed analysis of interface structure and passage probability

Abstract

We consider phase separation on the strip for the two-dimensional Ising model in the near-critical region. Within the framework of field theory, we find exact analytic results for certain two- and three-point correlation functions of the order parameter field. The analytic results for order parameter correlations, energy density profile, subleading corrections and passage probability density of the interface are confirmed by accurate Monte Carlo simulations we performed.