Classical topological paramagnetism

TL;DR

This paper introduces classical lattice models that exhibit topological phenomena similar to quantum topological phases, showing robust boundary effects in equilibrium classical systems and highlighting the role of simplicial cohomology for classification.

Contribution

It presents analytically tractable classical spin and rotor models with topological boundary phenomena, expanding the understanding of classical topological phases.

Findings

Classical models can exhibit boundary long-range order despite bulk being paramagnetic.

Simplicial cohomology classifies and analyzes classical topological phases.

Provides a new experimental approach to study topological spin systems.

Abstract

Topological phases of matter are one of the hallmarks of quantum condensed matter physics. One of their striking features is a bulk-boundary correspondence wherein the topological nature of the bulk manifests itself on boundaries via exotic massless phases. In classical wave phenomena analogous effects may arise; however, these cannot be viewed as equilibrium phases of matter. Here we identify a set of rules under which robust equilibrium classical topological phenomena exist. We write down simple and analytically tractable classical lattice models of spins and rotors in two and three dimensions which, at suitable parameter ranges, are paramagnetic in the bulk but nonetheless exhibit some unusual long-range or critical order on their boundaries. We point out the role of simplicial cohomology as a means of classifying, writing-down, and analyzing such models. This opens a new experimental route for studying strongly interacting topological phases of spins.