Classical Topological Order in Kagome Ice

TL;DR

This paper investigates classical topological order in kagome ice using Monte Carlo simulations, revealing how different update methods affect topological sector fluctuations and proposing susceptibility as a local probe.

Contribution

It introduces a non-local measure to characterize topological sectors and demonstrates how global versus local updates influence topological sector fluctuations.

Findings

Global loop updates cause topological sector fluctuations.

Local updates freeze the system into a single sector.

Susceptibility can distinguish between fluctuating and frozen sectors.

Abstract

We examine the onset of classical topological order in a nearest-neighbor kagome ice model. Using Monte Carlo simulations, we characterize the topological sectors of the groundstate using a non-local cut measure which circumscribes the toroidal geometry of the simulation cell. We demonstrate that simulations which employ global loop updates that are allowed to wind around the periodic boundaries cause the topological sector to fluctuate, while restricted local loop updates freeze the simulation into one topological sector. The freezing into one topological sector can also be observed in the susceptibility of the real magnetic spin vectors projected onto the kagome plane. The ability of the susceptibility to distinguish between fluctuating and non-fluctuating topological sectors should motivate its use as a local probe of topological order in a variety of related model and experimental systems.