Spin Softening in Models with Competing Interactions: A New High Anisotropy Expansion to All Orders

TL;DR

This paper develops an inverse spin anisotropy expansion to analyze how discrete spin models with competing interactions soften, revealing complex phase behaviors near multiphase points at zero temperature.

Contribution

It introduces a new high anisotropy expansion method applicable to models with competing interactions, enabling detailed study of phase transitions as spins become less constrained.

Findings

Identification of various phase behaviors including single first-order transitions and infinite series of commensurate phases.

Application to models like the chiral clock and p-state clock models with competing interactions.

Calculation of ground state phase diagrams near multiphase points at zero temperature.

Abstract

An expansion in inverse spin anisotropy, which enables us to study the behaviour of discrete spin models as the spins soften, is developed. In particular we focus on models, such as the chiral clock model and the $p$-state clock model with competing first and second neighbour interactions, where there are special multiphase points at zero temperature at which an infinite number of ground states are degenerate. The expansion allows calculation of the ground state phase diagram near these points as the spin anisotropy, which constrains the spin to take discrete values, is reduced from infinity. Several different behaviours are found, from a single first order phase boundary to infinite series of commensurate phases.