Free energy in spin glass models with conventional order

Abstract

Recently, [DOI:10.1007/s10955-023-03135-1] considered spin glass models with additional conventional order parameters characterizing single-replica properties. These parameters are distinct from the standard order parameter, the overlap, used to measure correlations between replicas. A ``min-max'' formula for the free energy was prescribed in [DOI:10.1007/s10955-023-03135-1]. We rigorously verify this prescription in the setting of vector spin glass models featuring additional deterministic spin interactions. Notably, our results can be viewed as a generalization of the Parisi formula for vector spin glass models in [DOI:10.1214/17-AOP1194], where the order parameter for self-overlap is already present.

18 pages; journal version

References in corpus (4)

• Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
• The mean field Ising model trough interpolating techniques
• On quantum and relativistic mechanical analogues in mean field spin models
• Revisiting the replica trick: Competition between spin glass and conventional order

Cited by in corpus (3)

• Directly observing replica symmetry breaking in a vector quantum-optical spin glass
• Hamilton-Jacobi equations from mean-field spin glasses
• Color symmetry and ferromagnetism in Potts spin glass