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, , 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, . The system has a line of continuous transition for this range of p from . 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 for p < 0.046(and for large for p > 0.954) even at zero temperature.