Ergodicity breaking in frustrated disordered systems: Replicas in mean-field spin-glass models

Abstract

We discuss ergodicity breaking in frustrated disordered systems with no apparent broken symmetry of the Hamiltonian and present a way how to amend it in the low-temperature phase. We demonstrate this phenomenon on mean-field models of spin glasses. We use replicas of the spin variables to test thermodynamic homogeneity of ergodic equilibrium systems. We show that replica-symmetry breaking reflects ergodicity breaking and is used to restore an ergodic state. We then present explicit asymptotic solutions for the Ising, Potts and $p$-spin glasses. Each of the models shows a different low-temperature behavior and the way the replica symmetry and ergodicity are broken.

arXiv comment11 pp, 2 figures, Invited talk at International Workshop on Relaxor Ferroelectrics XIV, Stirin; to appear in Phase Transitions

References in corpus (7)

• Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
• Mean-field solution of the Potts glass near the transition temperature to the ordered phase
• Stability of solutions of the Sherrington-Kirkpatrick model with respect to replications of the phase space
• Hierarchical solutions of the Sherrington-Kirkpatrick model: Exact asymptotic behavior near the critical temperature
• The Parisi formula completed
• Continuous replica-symmetry breaking in mean-field spin-glass models: Perturbation expansion without the replica trick
• Continuous RSB mean-field solution of the Potts glass