Bubble nucleation in disordered Landau-Ginzburg model

TL;DR

This paper studies bubble nucleation in a disordered Landau-Ginzburg model, analyzing symmetry breaking, instanton solutions, and an effective model for multiple nucleation processes at finite temperature.

Contribution

It introduces a novel effective model for describing multiple bubble nucleation events beyond the dilute instanton approximation in a disordered system.

Findings

Identification of N real instanton solutions below critical temperature

Development of an effective bosonic field model interacting with two-level systems

Analysis of symmetry breaking via replica saddle-point equations

Abstract

In this paper we investigate bubble nucleation in a disordered Landau-Ginzburg model. First we adopt the standard procedure to average over the disordered free energy. This quantity is represented as a series of the replica partition functions of the system. Using the saddle-point equations in each replica partition function, we discuss the presence of a spontaneous symmetry breaking mechanism. The leading term of the series is given by a large-N Euclidean replica field theory. Next, we consider finite temperature effects. Below some critical temperature, there are N real instantons-like solutions in the model. The transition from the false to the true vacuum for each replica field is given by the nucleation of a bubble of the true vacuum. In order to describe these irreversible processes of multiple nucleation, going beyond the diluted instanton approximation, an effective model is constructed, with one single mode of a bosonic field interacting with a reservoir of N identical two-level systems.