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

TL;DR

This paper investigates a p-spin model with random crystal fields, revealing complex phase transition behavior including multiple first-order transitions, a triple point, a critical point, and a Gardner-like transition for all finite p ≥ 3.

Contribution

It uncovers the rich phase diagram of the p-spin model with quenched disorder, showing multiple transitions and a Gardner-like transition for finite p, and distinct behavior as p approaches infinity.

Findings

Multiple lines of first-order transitions at finite temperature for all p ≥ 3.

Existence of a triple point and a critical point depending on the crystal field strength.

Observation of a Gardner-like transition upon increasing temperature for finite p.

Abstract

We study a $p$-spin model with ferromagnetic coupling and quenched random-crystal fields for $p \ge 3$ for spin-1 systems. We find that the model has lines of first order transitions at finite temperature $(T)$ for all $p \ge 3$. For bimodal distribution of the random-crystal field these lines meet at a \emph{triple point} for weak strength of the crystal field $(\Delta)$. Beyond a critical strength of $\Delta$, they do not meet and one of the lines ends at a \emph{critical point} $(T_c)$. Interestingly, we find that on increasing $T$ from $T_c$ keeping other parameters fixed, the system undergoes one more transition which is first order in its character. The system thus exhibits a Gardner like transition for a range of parameters for all finite $p \ge 3$. For $p \to \infty$ the model behaves differently and there is only one random first order transition at $T = 0$.