Three-dimensional Z( N) lattice gauge models at large N

Abstract

An upper bound is derived for the Z(2) vortex free energy in three-dimensional Z( N) lattice gauge models ( N even). This is proved that the inverse temperature β c( N) is unbounded as N goes to infinity, and to argue that it goes at least as √ N is it is proved that the three-dimensional SU( N) model confines static quarks as N → ∞ with β SU( N) fixed.