Replica solution of the Random Energy Model

TL;DR

This paper presents a replica technique that avoids analytic continuation and symmetry breaking, providing a straightforward and rigorous solution for the average free energy of the Random Energy Model.

Contribution

It introduces an alternative replica method that simplifies calculations and yields rigorous results without replica symmetry breaking.

Findings

Successfully derives the average free energy of the REM

Demonstrates the method's simplicity and rigor

Avoids complex analytic continuation procedures

Abstract

The alternative replica technique which involve summation over all integer momenta of the partition function and which does not require analytic continuation to non-integer values of the replica parameter $n$ is discussed. In terms of this technique (which does not involve any replica symmetry breaking "magic operations") rigorous solution for the average free energy of the Random Energy Model is recovered in a very simple way.