Journal of Statistical Physics, Vol. 23, No. 5, 1980. p. 609-625.
With the aid of the differential real-space method we derive exact renormalization group (RG) equations for the Gaussian model in d dimensions. The equations involve d + 1 spatially dependent nearest-neighbor interactions. We locate a critical fixed point and obtain the exact thermal critical index Y_t = 2. A special trajectory of the full nonlinear RG transformation is found and the free energy of the corresponding initial state calculated.