Group structure analysis for classical lattice systems with constraints: I. General properties

The group structure associated with lattice systems without constraints is extended to systems with constraints and some of its physical consequences are investigated. In particular low- and high-temperature expansions, equilibrium equations and duality transformations are analyzed within this framework. It is shown that a large class of systems with constraints whose configuration space has a group structure are “equivalent” to systems without constraints. These structures are illustrated with several examples.