Phase diagram for the spin-3/2 quantum ferromagnetic Blume-Capel model in a transverse crystal field: an approximation at the mean-field level

TL;DR

This study maps the complex phase diagram of the spin-3/2 ferromagnetic Blume-Capel model in a transverse field using mean-field approximation, revealing rich multicritical phenomena not previously characterized.

Contribution

It provides the first comprehensive phase diagram analysis of this quantum spin model using free energy-based mean-field methods, uncovering multicritical points.

Findings

Rich phase diagram with multiple critical points

Identification of tricritical and tetracritical points

Behavior of magnetization across temperature and field variations

Abstract

We investigate the phase diagram for the spin-$3/2$ ferromagnetic Blume-Capel model in a transverse crystal field using the standard mean-field approximation within the framework of Bogoliubov inequality for free energy. We draw a very rich phase diagram with first- and second-order transition lines; tricritical and tetracritical points; critical endpoint of order 2 and double critical endpoint. Additionally, the behaviour of magnetisation as a function of temperature over a wide range of values of both longitudinal and transverse crystal fields is also analysed. To the best of our knowledge, this quantum spin model has only been studied employing an effective field theory, which in turn was not able to characterise completely the multicritical phenomena in its phase diagram, because that procedure is not based on free energy. Thus, our findings on the phase diagram for the present model are novel as they have been not previously reported.