<i>p</i>-spin-interaction spin-glass models: Connections with the structural glass problem

TLDR

The mean‑field dynamical theory’s mathematical structure closely parallels recent dynamical theories of the structural glass transition. The study investigates both static and dynamical theories of the mean‑field p‑spin (p>2) interaction spin‑glass model. By reinterpreting the equilibrium solution, the authors link the dynamical transition to the equilibrium theory. The broken‑replica‑symmetry equilibrium solution predicts a glass transition at \(T_g'\) with a discontinuous Edwards‑Anderson order parameter, no latent heat, and a discontinuous specific heat, while the dynamical theory predicts a continuous slowing down and a higher glass transition temperature \(T_g>T_g'\).

Abstract

The static and the dynamical theories for the mean-field p-spin (p&gt;2) interaction spin-glass model are studied. A broken-replica-symmetric equilibrium solution leads to a glass transition at a temperature ${T}_{g}^{\mathcal{'}}$ where the Edwards-Anderson order parameter is discontinuous but where there is no latent heat and there is a discontinuous specific heat. The dynamical theory leads to a continuous slowing down and predicts a glass transition at ${T}_{g}$&gt;${T}_{g}^{\mathcal{'}}$. A reinterpretation of the equilibrium solution allows us to relate the dynamical transition to the equilibrium theory. The mathematical structure of the mean-field dynamical theory is closely related to certain recent dynamical theories of the structural glass transition.