Gaussian smearing of spin weight functions in models of phase transitions

By smearing with a Gaussian distribution a family of single-spin weight functions is constructed which interpolates between an arbitrary single-spin distribution and a pure Gaussian. The observation of Baker and Bishop (1982) concerning the factorisability of the partition function of the double Gaussian model remains valid for all Gaussian-smeared models. The effects of smearing Gaussian and spherical weight functions are studied in further detail.