Replica method and finite volume corrections

TL;DR

This paper introduces a method to compute finite volume corrections in replica symmetry broken systems, revealing additional fluctuation-driven modifications to mean field free energy results.

Contribution

It proposes a novel approach to derive replica broken results rigorously by accounting for fluctuations in replica block sizes.

Findings

Finite volume corrections modify naive mean field results.

Additional corrections are linked to fluctuations in replica block sizes.

The method offers a new pathway for rigorous derivation of replica symmetry breaking results.

Abstract

In this note we introduce a method to calculate the finite volume corrections to the mean field results for the free energy when replica symmetry is broken at one-step. We find that the naive results are modified by the presence of additional corrections: these corrections can be interpreted as arising from fluctuations in the size of the blocks in the replica approach. The computation suggests a new approach for deriving the replica broken results in a rigorous way.