On the Universality of the Superconcentration in Mixed p-Spin Models

Consider the mixed p-spin models with general environments such that the covariance of Hamiltonian process is non-negative. In this paper, we prove the universality of the superconcentration phenomenon. Precisely, we show that the variance of the free energy grows sublinearly in the size of its expectation when the disordered random variable satisfies some moment matching conditions. Additionally, we also study the universality of first and second moments of the free energy of a spin glass model on general hypergraphs.