Group structure analysis for classical lattice systems with constraints

The Asano-Ruelle method is used to discuss the zeroes of the partition function of arbitrary lattice systems with constraints. The group structure associated with these systems yields necessary and sufficient conditions to build up the partition function by Asano contractions. For a large class of systems with constraints, uniqueness of the symmetric equilibrium state, as well as analyticity properties of the free energy and the correlation functions, is established at sufficiently low temperature. Explicit analyticity domains are obtained for several models with constraints. Some properties of power sets are derived.