Bogomol'nyi Bounds for Two-Dimensional Lattice Systems

TL;DR

This paper develops lattice models for the O(3) sigma and abelian Higgs systems in two dimensions that preserve Bogomol'nyi bounds, enhancing the stability of topological solitons on the lattice.

Contribution

It introduces lattice formulations of these models that maintain the Bogomol'nyi bounds, a feature previously limited to continuum theories.

Findings

Lattice models with preserved Bogomol'nyi bounds are constructed.

Topological solitons exhibit increased stability on the lattice.

The approach bridges continuum topological bounds and discrete lattice systems.

Abstract

The O(3) sigma model and abelian Higgs model in two space dimensions admit topological (Bogomol'nyi) lower bounds on their energy. This paper proposes lattice versions of these systems which maintain the Bogomol'nyi bounds. One consequence is that instantons/solitons/vortices on the lattice then have a high degree of stability.