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On free energy of non-convex multi-species spin glasses

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arxiv 2411.13342 v1 pith:6KQCD4DD submitted 2024-11-20 cond-mat.dis-nn math.PR

classification cond-mat.dis-nnmath.PR
keywords non-convexspinenergyfreemodelsmulti-speciesvectorglass
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In [arXiv:2311.08980], it was shown that if the limit of the free energy in a non-convex vector spin glass model exists, it must be a critical value of a certain functional. In this work, we extend this result to multi-species spin glass models with non-convex interactions, where spins from different species may lie in distinct vector spaces. Since the species proportions may be irrational and the existence of the limit of the free energy is not generally known, non-convex multi-species models cannot be approximated by vector spin models in a straightforward manner, necessitating more careful treatment.

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  1. Balanced multi-species spin glasses

    math.PR 2025-07 conditional novelty 7.0 of 10

    A lower bound shows balanced multi-species spin glasses have free energy at least that of a single-species model with variance-matched couplings, and this bound is sharp in several regimes.

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