First steps of a nucleation theory in disordered systems

TL;DR

This paper introduces a field theoretical approach to understand nucleation and phase coexistence in finite-dimensional disordered glassy systems, focusing on disordered p-spin models with finite interaction range.

Contribution

It develops a microscopic field theory formalism for nucleation in disordered systems, linking metastability and phase coexistence to inhomogeneous solutions of field equations.

Findings

Establishes a connection between metastability and inhomogeneous solutions.

Provides a framework for studying nucleation in finite-dimensional glassy systems.

Analyzes simple solutions related to phase coexistence.

Abstract

We devise a field theoretical formalism for a microscopic theory of nucleation processes and phase coexistence in finite dimensional glassy systems. We study disordered $p$-spin models with large but finite range of interaction. We work in the framework of glassy effective potential theory which in mean-field is a non-convex, two minima function of the overlap. We will associate metastability and phase coexistence with the existence of space inhomogeneous solution of suitable field equations and we will study the simplest of such solutions.