Renormalization-group transformations under strong mixing conditions: Gibbsianness and convergence of renormalized interactions

In this paper we study a renormalization-group map: the block averaging tra nsformation applied to Gibbs measures relative to a class of finite-range l attice gases, when suitable strong mixing conditions are satisfied. Using a block decimation procedure, cluster expansion. and detailed comparison bet ween statistical ensembles, we are able to prove Gibbsianness and convergen ce to a trivial (i.e., Gaussian and product) fixed point. Our results apply to the 2D standard Ising model dr any temperature above the critical one a nd arbitrary magnetic field.