Spin cones in random-field XY models

TL;DR

This paper investigates the ground state spin configurations in the XY model with quenched random fields on a fully connected graph, revealing cone-shaped arrangements and phase transitions depending on the type of disorder and field strength.

Contribution

It provides a detailed analysis of spin arrangements in the XY model with quenched disorder, introducing new insights into the formation of cones and phase transitions in such systems.

Findings

Spins form a cone for small field-to-coupling ratios.

Cone angle widens with increasing ratio until a phase transition occurs.

Different disorder types lead to distinct phase behaviors.

Abstract

We determine the arrangement of spins in the ground state of the XY model with quenched, random fields, on a fully connected graph. Two types of disordered fields are considered, namely randomly oriented magnetic fields, and randomly oriented crystal fields. Orientations are chosen from a uniformly isotropic distribution, but disorder fluctuations in each realization of a finite system lead to a breaking of rotational symmetry. The result is an interesting pattern of spin orientations, found by solving a system of coupled, nonlinear equations within perturbation theory and also by exact numerical continuation. All spins lie within a cone for small enough ratio of field to coupling strength, with an interesting distribution of spin orientations, with peaks at the cone edges. The orientation of the cone depends strongly on the realization of disorder, but the opening angle does not. In the case of random magnetic fields, the cone angle widens as the ratio increases till a critical value at which there is a first order phase transition and the cone disappears. With random crystal fields, there is no phase transition and the cone angle approaches $180^\circ$ for large values of the ratio. At finite low temperatures, Monte-Carlo simulations show that the formation of a cone and its subsequent alignment along the equilibrium direction occur on two different time scales.