Competing interactions in the XYZ model

TL;DR

This paper investigates the complex interplay of anisotropy, exchange modulations, and magnetic fields in the XYZ chain, revealing an Ising critical line caused by competing perturbations using bosonization and numerical methods.

Contribution

It introduces a detailed analysis of the XYZ model with multiple competing interactions, identifying critical behavior and phase transitions.

Findings

Discovery of an Ising critical line in the XYZ model.

Identification of competing relevant perturbations affecting phase transitions.

Application of bosonization and Lanczos techniques to analyze the model.

Abstract

We study the interplay between a XY anisotropy $\gamma$, exchange modulations and an external magnetic field along the z direction in the XYZ chain using bosonization and Lanczos diagonalization techniques. We find an Ising critical line in the space of couplings which occur due to competing relevant perturbations which are present. More general situations are also discussed.