Multicritical behavior of the two-dimensional transverse Ising metamagnet in a longitudinal magnetic field

TL;DR

This study investigates the phase transitions and critical behavior of a two-dimensional transverse Ising metamagnet in magnetic fields using a mean-field approach, revealing diverse transition types and tricritical points.

Contribution

It introduces a mean-field variational method with a single-spin cluster to analyze the phase diagrams of the model, highlighting differences from effective field theory results.

Findings

Identified regions with only second-order transitions.

Found regions with only first-order transitions.

Discovered tricritical points and no reentrant behavior at low temperatures.

Abstract

Magnetic phenomena of the superantiferromagnetic Ising model in both uniform longitudinal ($H$) and transverse ($\Omega $) magnetic fields are studied by employing a mean-field variational approach based on Peierls-Bogoliubov inequality for the free energy. A single-spin cluster is used to get the approximate thermodynamic properties of the model. The phase diagrams in the magnetic fields and temperature ($T$) planes, namely, $H-T$ and $\Omega-T$, are analyzed on an anisotropic square lattice for some values of the ratio $\alpha=J_{y}/J_{x}$, where $J_x$ and $J_y$ are the exchange interactions along the $x$ and $y$ directions, respectively. Depending on the range of the Hamiltonian parameters, one has only second-order transition lines, only first-order transition lines, or first- and second-order transition lines with the presence of tricritical points. The corresponding phase diagrams show no reentrant behavior along the first-order transition lines at low temperatures. These results are different from those obtained by using Effective Field Theory with the same cluster size.