On a Dynamical-Like Replica-Symmetry-Breaking Scheme for the Spin Glass

TL;DR

This paper compares traditional Parisi replica-symmetry breaking with a dynamical-like RSB scheme for spin glasses, showing the latter yields physically consistent positive free-energy costs for boundary twists.

Contribution

It introduces a dynamical-like RSB scheme that maintains positive multiplicities, resolving unphysical results of the conventional Parisi RSB in spin glass free-energy calculations.

Findings

Dynamical RSB yields positive twist free energy.

Traditional Parisi RSB results in negative multiplicities.

Both schemes agree on free energies and observables for homogeneous systems.

Abstract

Considering the unphysical result obtained in the calculation of the free-energy cost for twisting the boundary conditions in a spin glass, we trace it to the negative multiplicities associated with the Parisi replica-symmetry breaking (RSB). We point out that a distinct RSB, that keeps positive multiplicities, was proposed long ago, in the spirit of an ultra-long time dynamical approach due to Sompolinsky. For an homogeneous bulk system, both RSB schemes are known to yield identical free energies and observables. However, using the dynamical RSB, we have recalculated the twist free energy at the mean-field level. The free-energy cost of this twist is, as expected, positive in that scheme, as it should be.