The spherical $2+p$ spin glass model: an exactly solvable model for glass to spin-glass transition

Abstract

We present the full phase diagram of the spherical $2+p$ spin glass model with $p\geq 4$. The main outcome is the presence of a new phase with both properties of Full Replica Symmetry Breaking (FRSB) phases of discrete models, e.g, the Sherrington-Kirkpatrick model, and those of One Replica Symmetry Breaking (1RSB). The phase, which separates a 1RSB phase from FRSB phase, is described by an order parameter function $q(x)$ with a continuous part (FRSB) for $x<m$ and a discontinuous jump (1RSB) at $x=m$. This phase has a finite complexity which leads to different dynamic and static properties.