# Spontaneous symmetry breaking in fermionic random matrix model

## TL;DR

This paper investigates a fermionic random matrix model analogous to the SYK model, demonstrating spontaneous symmetry breaking at large N and exploring implications for fermionic spin glass phases.

## Contribution

It introduces the analysis of spontaneous symmetry breaking in a fermionic random matrix model using the Bogoliubov quasi-averages approach.

## Key findings

- Replica-off-diagonal correlations vanish at finite N
- Correlations do not vanish in the large N limit due to symmetry breaking
- Potential relevance to fermionic spin glass phase studies

## Abstract

A fermionic random matrix model, which is a 0-dimensional version of the SYK model with replicas, is considered. The replica-off-diagonal correlation functions vanish at finite N, but we show that they do not vanish in the large N limit due to spontaneous symmetry breaking. We use the Bogoliubov quasi-averages approach to studying phase transitions. The consideration may be relevant to the study of the problem of existence of the spin glass phase in fermionic models.