On the self-overlap in vector spin glasses

Abstract

We consider vector spin glass models with self-overlap correction. Since the limit of free energy is an infimum, we use arguments analogous to those for generic models to show the following: (1) the averaged self-overlap converges; (2) the self-overlap concentrates; (3) the infimum optimizes over paths whose right endpoints are the limit of self-overlap. Lastly, using these, we directly verify the equivalence between the variational formula obtained in Chen [Electron. J. Probab. 28, 1 (2023)] and Panchenko’s generalized Parisi formula in Panchenko [Ann. Probab. 46(2), 865 (2018)].