Free energy in spin glass models with conventional order
arXiv:2401.10223 · doi:10.1007/s10955-024-03266-z
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
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