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, $P(\hat{I}{”}_i)=p\hat{I}´(\hat{I}{”}_i-\hat{I}”)+(1-p)\hat{I}´(\hat{I}{”}_i+\hat{I}”)$, 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, $\hat{I}”$. The system has a line of continuous transition for this range of $p$ from $-\infty <\hat{I}”<\infty$. 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 $\hat{I}”$ for $p<0.046$(and for large $-\hat{I}”$ for $p>0.954$) even at zero temperature.

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