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

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.

arXiv commentREVTeX4, 13 pages, 8 EPS figures

References in corpus (4)

• On the formal equivalence of the TAP and thermodynamic methods in the SK model
• Numerical study of metastable states in Ising spin glasses
• Stability of solutions of the Sherrington-Kirkpatrick model with respect to replications of the phase space
• Replica trick with real replicas: A way to build in thermodynamic homogeneity

Cited by in corpus (3)

• Mean-field solution of the Potts glass near the transition temperature to the ordered phase
• Small-world hypergraphs on a bond-disordered Bethe lattice
• Incompleteness of the Thouless, Anderson, and Palmer mean-field description of the spin-glass phase