Bogomol'nyi Bounds for Two-Dimensional 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.

Comments: 17 pages, plainTeX, figures not included, to be published in Commun Math Phys