A puzzle on fluctuations of weights in spin glasses

TL;DR

This paper investigates fluctuations in the internal energy of mean field spin glass models with one-step replica symmetry breaking, showing that both the height and location of the breakpoint fluctuate, affecting the allowed order parameter fluctuations.

Contribution

It demonstrates that considering fluctuations in both the height and position of the replica symmetry breaking breakpoint is essential for accurate energy fluctuation calculations.

Findings

Fluctuations in the breakpoint's height and location are crucial for correct energy fluctuation results.

The derived fluctuations align with known specific heat results.

The phenomenon does not occur in models with infinite order replica symmetry breaking.

Abstract

In certain mean field models for spin glasses there occurs a one step replica symmetry breaking pattern. As an example of general $1/N$-corrections in such systems, the fluctuations in the internal energy are calculated. For this specific quantity the outcome is known from the specific heat. It is shown that the correct result can be derived by assuming that the both the height and the location of the breakpoint fluctuate. This effect enlarges the commonly considered space of allowed fluctuations of the order parameter in loop calculations for short range spin glasses of this type. The phenomenon does not occur in spin glasses with infinite order replica symmetry breaking.