Quenched free energy in random matrix model

TL;DR

This paper calculates the quenched free energy in a Gaussian random matrix model directly, revealing its monotonic temperature dependence and entropy behavior, without relying on the replica trick.

Contribution

It introduces a direct evaluation method for quenched free energy in random matrix models, avoiding the replica trick.

Findings

Quenched free energy is monotonic with temperature.

Entropy approaches log N at high temperature.

Entropy vanishes at zero temperature.

Abstract

We compute the quenched free energy in the Gaussian random matrix model by directly evaluating the matrix integral without using the replica trick. We find that the quenched free energy is a monotonic function of the temperature and the entropy approaches $\log N$ at high temperature and vanishes at zero temperature.