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

TL;DR

This study analyzes the Blume-Capel model with random crystal fields on a complete graph, revealing the destruction of first order transitions within a specific probability range and the emergence of continuous transitions.

Contribution

It provides an exact solution showing how randomness in crystal fields alters phase transition types in the Blume-Capel model on a fully connected graph.

Findings

First order transition is destroyed for 0.046<p<0.954.

A line of continuous transition exists within this p-range.

Phase diagram resembles the pure model outside this p-range.

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.