  In this paper we study a renormalization-group map: the block averaging
transformation applied to Gibbs measures relative to a class of finite range
lattice gases, when suitable strong mixing conditions are satisfied. Using
block decimation procedure, cluster expansion (like in [HK]) and detailed
comparison between statistical ensembles, we are able to prove Gibbsianess and
convergence to a trivial (i.e. Gaussian and product) fixed point. Our results
apply to 2D standard Ising model at any temperature above the critical one and
arbitrary magnetic field.
