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

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 $T=0$.

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Cited by in corpus (1)

• Exactly solvable dynamics and signatures of integrability in an infinite-range many-body Floquet spin system