# Spontaneous symmetry breaking in replica field theory

## TL;DR

This paper investigates spontaneous symmetry breaking in a disordered Euclidean $\

## Contribution

It demonstrates the presence of spontaneous symmetry breaking in a replica field theory using saddle-point and large-N techniques.

## Key findings

- Spontaneous symmetry breaking occurs in the disordered model.
- Large-N Euclidean replica field theory describes the dominant replica partition function.
- Existence of N instantons at low temperature.

## Abstract

In this paper we discuss a disordered $d$-dimensional Euclidean $\lambda\varphi^{4}$ model. The dominant contribution to the average free energy of this system is written as a series of the replica partition functions of the model. In each replica partition function, using the saddle-point equations and imposing the replica symmetric ansatz, we show the presence of a spontaneous symmetry breaking mechanism in the disordered model. Moreover, the leading replica partition function must be described by a large-$N$ Euclidean replica field theory. We discuss finite temperature effects considering periodic boundary condition in Euclidean time and also using the Landau-Ginzburg approach. In the low temperature regime we prove the existence of $N$ instantons in the model.