Free energy in spin glass models with conventional order

Author:

Hong-Bin Chen

Keyword:

Condensed Matter, Disordered Systems and Neural Networks, Disordered Systems and Neural Networks (cond-mat.dis-nn), Mathematical Physics (math-ph), Probability (math.PR)

journal:

date:

2024-01-18 00:00:00

Abstract

Recently, [arXiv:2302.01361] considered spin glass models with additional conventional order parameters characterizing single-replica properties. These parameters are distinct from the standard order parameter used to measure correlations between replicas. A "min-max" formula for the free energy was prescribed in [arXiv:2302.01361]. 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 [arXiv:1512.04441], where the order parameter for self-overlap is already present.

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