Ferromagnetic phases due to competing short- and long-range interactions in the spin-S Blume-Capel model

TL;DR

This paper investigates the complex phase behavior of the spin-$S$ Blume-Capel model with competing ferromagnetic and antiferromagnetic interactions, revealing new ferromagnetic phases and intricate phase diagrams for both integer and half-integer spins.

Contribution

It introduces a detailed analysis of the phase diagrams of the spin-$S$ Blume-Capel model with competing interactions, highlighting new ferromagnetic phases and their topological features.

Findings

Discovery of new ferromagnetic phases in the phase diagrams.

Complex topologies of phase diagrams at finite temperatures.

Emergence of phases from first-order transition frontiers.

Abstract

We broaden the study of the statistical physics of the spin-$S$ Blume-Capel model with ferromagnetic mean-field interactions $J$ in competition with short-range antiferromagnetic interactions $K$ in a linear chain in the thermodynamic limit. This work describes the critical behavior of the model when the $S$ takes a half integer and an integer value. In both cases the phase diagrams exhibit new ferromagnetic phases (for certain values of $K$) enclosed by branches emerging from the first-order frontiers of the pure ferromagnetic model. For finite temperatures the complex topologies were obtained by numerical minimization of the free energy.