Stepwise Positional-Orientational Order and the Multicritical-Multistructural Global Phase Diagram of the s=3/2 Ising Model from Renormalization-Group Theory

TL;DR

This paper uses renormalization-group theory to analyze the complex phase diagram of the spin-3/2 Ising model, revealing multiple phases, critical points, and reentrant behaviors with rich structural properties.

Contribution

It provides a detailed global phase diagram of the spin-3/2 Ising model, including novel multicritical points and the identification of a plastic crystal sequence, using renormalization-group analysis.

Findings

Eight different ordered and disordered phases identified.

Presence of multiple critical and multicritical points, including bicritical and tetracritical points.

Observation of a plastic crystal sequence with sequential positional and orientational order.

Abstract

The spin-3/2 Ising model, with nearest-neighbor interactions only, is the prototypical system with two different ordering species, with concentrations regulated by a chemical potential. Its global phase diagram, obtained in d=3 by renormalization-group theory in the Migdal-Kadanoff approximation or equivalently as an exact solution of a d=3 hierarchical lattice, with flows subtended by 40 different fixed points, presents a very rich structure containing eight different ordered and disordered phases, with more than fourteen different types of phase diagrams in temperature and chemical potential. It exhibits phases with orientational and/or positional order. It also exhibits quintuple phase transition reentrances. Universality of critical exponents is conserved across different renormalization-group flow basins, via redundant fixed points. One of the phase diagrams contains a plastic crystal sequence, with positional and orientational ordering encountered consecutively as temperature is lowered. The global phase diagram also contains double critical points, first-order and critical lines between two ordered phases, critical endpoints, usual and unusual (inverted) bicritical points, tricritical points, multiple tetracritical points, and zero-temperature criticality and bicriticality. The 4-state Potts permutation-symmetric subspace is contained in this model.