Phase Diagram of the $J_1$ - $J_2$ Frustrated Anisotropic Antiferromagnet with Spin $S=1$ on the Quadratic Lattice

TL;DR

This study maps the phase diagram of a spin-1 frustrated antiferromagnet on a quadratic lattice, revealing phase boundaries, tricritical points, and the effects of cluster size and anisotropy using cluster approximations.

Contribution

It introduces a cluster approximation approach to analyze the phase diagram of a spin-1 frustrated antiferromagnet with anisotropy, comparing results across cluster sizes and with classical mean-field theory.

Findings

Identification of phase boundaries for different magnetic phases

Detection of tricritical and triple points in the phase diagram

Comparison showing the influence of cluster size and anisotropy on results

Abstract

In the paper the phase diagram of $J_1-J_2$ frustrated antiferromagnet with spin $S=1$ and single-ion anisotropy is studied on the planar quadratic lattice in the cluster approximation. The Bogolyubov inequality is adopted for the Gibbs energy calculation for the case of $2 \times 2$ and $4 \times 4$ clusters. On this basis, the ranges of existence of the anfiferromagnetic, superantiferromagnetic and paramagnetic phases are investigated for the antiferromagnetic nearest-neighbour ($J_1<0$) and next-nearest-neighbour ($J_2<0$) interactions. In particular, the occurrence of tricritical and triple points is discussed and a comparison between the results for $2 \times 2$ and $4 \times 4$ clusters is made. The results are also compared with the classical MFA method, adopted here for the model in question, as well as with selected literature results for particular choices of interaction parameters.