Thermodynamic origin of order parameters in mean-field models of spin glasses

TL;DR

This paper explores the thermodynamic basis of the hierarchical order parameters in mean-field spin glass models, linking their structure to inter-replica susceptibilities that resolve metastable state degeneracies.

Contribution

It derives a configurationally dependent free energy incorporating local magnetizations and susceptibilities, revealing the origin of order parameter hierarchy from inter-replica interactions.

Findings

Hierarchy of order parameters stems from inter-replica susceptibilities.

Susceptibilities lift degeneracy among metastable states.

The approach restores thermodynamic homogeneity in the free energy.

Abstract

We analyze thermodynamic behavior of general $n$-component mean-field spin glass models in order to identify origin of the hierarchical structure of the order parameters from the replica-symmetry breaking solution. We derive a configurationally dependent free energy with local magnetizations and averaged local susceptibilities as order parameters. On an example of the replicated Ising spin glass we demonstrate that the hierarchy of order parameters in mean-field models results from the structure of inter-replica susceptibilities. These susceptibilities serve for lifting the degeneracy due to the existence of many metastable states and for recovering thermodynamic homogeneity of the free energy.