# Emergence of a bicritical end point in the random crystal field Blume-Capel model

## TL;DR

This paper explores how disorder affects the phase diagram of the Blume-Capel model, revealing a transition from tricritical to bicritical end points as disorder strength increases.

## Contribution

It introduces the phase diagram of the disordered Blume-Capel model, highlighting the emergence of bicritical end points with increasing disorder.

## Key findings

- Tricritical point exists only at weak disorder.
- Bicritical end point appears at higher disorder levels.
- Phase diagram complexity increases with disorder strength.

## Abstract

We obtain the phase diagram for the Blume-Capel model with bimodal distribution for random crystal fields, in the space of three fields: temperature, crystal field and magnetic field. We find that three critical lines meet at a tricritical point, but only for weak disorder. As disorder strength increases there is no tricritical point in the phase diagram. We instead find a bicritical end point, where only two of the critical lines meet on a first order surface in the H=0 plane. For intermediate strengths of disorder, the phase diagram has critical end points along with the bicritical end point. One needs to look at the phase diagram in the space of three fields to identify various such multicritical points.