Spin one $p$-spin glass: the Gardner transition

Abstract

We examine the phase diagram of the p-spin mean field glass model in the spin one case, that is when S = 0, +1, −1. For large p the model is solved exactly. The analysis reveals that the phase diagram is in some way similar to that of Ising spins. However, as we show, the quadrupolar regular ordering as well as qudrupolar glass order are present now. The temperature of the Gardner 1RSB -FRSB transition is obtained explicitly for large p. The case of higher spins is discussed briefly.

Multiple transitions in an infinite range p-spin random-crystal field Blume Capel model

“…This T f is associated with the first order transition as m ≈ r and m = 0 below and above T f which can be seen from the plot of f (m) at T = 0.1 and 0.16 respectively. Notably, these successive second and first order transitions of the order parameter m with T are quite similar to the Gardner transition [23] observed in a system of p-spin interacting Ising [23], Potts [25] and spin-1 [32] spin glass. The first order transiton in these systems is associated with no latent heat which is sharply in constrast with pRCBCM where we observe a finite latent heat.…”