Absence of first order transition in the random crystal field Blume-Capel model on a fully connected graph

Abstract

In this paper we solve the Blume-Capel model on a complete graph in the presence of random crystal field with a distribution, $P({\Delta }_i)=p\delta ({\Delta }_i-\Delta )+(1-p)\delta ({\Delta }_i+\Delta )$, using large deviation techniques. We find that the first order transition of the pure system is destroyed for $0.046<p<0.954$ for all values of the crystal field, $\Delta$. The system has a line of continuous transition for this range of $p$ from $-\infty <\Delta <\infty$. For values of $p$ outside this interval, the phase diagram of the system is similar to the pure model, with a tricritical point separating the line of first order and continuous transitions. We find that in this regime, the order vanishes for large $\Delta$ for $p<0.046$(and for large $-\Delta$ for $p>0.954$) even at zero temperature.

replaced with the accepted version; to be published in J. Phys. A

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• Solution of the random field $XY$ magnet on a fully connected graph
• Anisotropy driven reversal of magnetisation in Blume-Capel ferromagnet: A Monte Carlo study
• Multiple transitions in an infinite range p-spin random-crystal field Blume Capel model
• Phase transitions in XY models with randomly oriented crystal fields
• Ensemble dependence of the critical behavior of a system with long-range interaction and quenched randomness