Phase separation and interface structure in two dimensions from field theory

TL;DR

This paper provides an exact field theoretical analysis of phase separation and interface structures in two-dimensional systems below criticality, recovering known results for the Ising model and extending to Potts models and percolation.

Contribution

It offers a unified field theoretical framework for describing interface behavior and phase separation in 2D systems, including new results on branching deviations and cluster density profiles.

Findings

Exact magnetization profiles in 2D below criticality.

Gaussian behavior of interfaces in the infrared limit.

Leading deviations due to branching in Potts models.

Abstract

We study phase separation in two dimensions in the scaling limit below criticality. The general form of the magnetization profile as the volume goes to infinity is determined exactly within the field theoretical framework which explicitly takes into account the topological nature of the elementary excitations. The result known for the Ising model from its lattice solution is recovered as a particular case. In the asymptotic infrared limit the interface behaves as a simple curve characterized by a gaussian passage probability density. The leading deviation, due to branching, from this behavior is also derived and its coefficient is determined for the Potts model. As a byproduct, for random percolation we obtain the asymptotic density profile of a spanning cluster conditioned to touch only the left half of the boundary.