New approximation schemes for lattice theories

We describe a class of approximation procedures which is applicable to a variety of lattice theories including lattice gauge theories. The approach is nonperturbative in the temperature or its inverse. The low-order approximants are expected to be most reliable at low temperatures. As examples we approximate the free energy of the classical x-y model and of Abelian gauge fields on a lattice in two ways, one of which gives us monotonically converging bounds on the free energy