# Mean-field theory for confinement transitions and magnetization plateaux in spin ice

## TL;DR

This paper develops a mean-field theory to analyze phase transitions in classical spin ice under magnetic fields, revealing a phase diagram with Coulomb phases and magnetization plateaux, highlighting the generic lobe structure in Coulomb spin liquids.

## Contribution

It introduces a novel mean-field approach to study confinement and topological effects in spin ice, connecting phase diagram features to Bose-Hubbard-like models.

## Key findings

- Identification of a phase diagram with Coulomb and magnetization plateau phases
- Discovery of a lobe structure in the phase diagram similar to Bose-Hubbard models
- Demonstration of the generic nature of this structure in Coulomb spin liquids

## Abstract

We study phase transitions in classical spin ice at nonzero magnetization, by introducing a mean-field theory designed to capture the interplay between confinement and topological constraints. The method is applied to a model of spin ice in an applied magnetic field along the [100] crystallographic direction and yields a phase diagram containing the Coulomb phase as well as a set of magnetization plateaux. We argue that the lobe structure of the phase diagram, strongly reminiscent of the Bose-Hubbard model, is generic to Coulomb spin liquids.