Analysis of a fully packed loop model arising in a magnetic Coulomb phase

TL;DR

This paper analyzes the statistical properties of fully-packed two-color loop models in three dimensions arising in Coulomb phases of spin ice, comparing them to 2D models and discussing implications for experiments.

Contribution

It provides a detailed analysis of three-dimensional fully-packed loop models in Coulomb phases, highlighting differences from 2D models and exploring flux line behavior.

Findings

Loops avoid themselves and same-color loops, affecting their statistics.

Flux lines behave as Dirac strings, revealing emergent gauge field properties.

Results have implications for related models and experimental observations.

Abstract

The Coulomb phase of spin ice, and indeed the Ic phase of water ice, naturally realise a fully-packed two-colour loop model in three dimensions. We present a detailed analysis of the statistics of these loops, which avoid themselves and other loops of the same colour, and contrast their behaviour to an analogous two-dimensional model. The properties of another extended degree of freedom are also addressed, flux lines of the emergent gauge field of the Coulomb phase, which appear as "Dirac strings" in spin ice. We mention implications of these results for related models, and experiments.