Approximate Renormalization Group Based on the Wegner-Houghton Differential Generator

We give an approximate renormalization-group formulation which parallels that of Wilson. The group generator represents the momentum-independent limit of the differential generator of Wegner and Houghton. The eigenfunctions near the Gaussian point are computed for all spin dimensions n and lattice dimensions d, including $d=2$. The nontrivial fixed-point Hamiltonian in dimensions near d=2O(O-1), together with the eigenvalues near that nontrivial fixed point, are found explicitly to first order in εO≡O(2-d)+d for all values of n and the order O. Odd-dominated Ising systems and corresponding expansions in ε_O-1/2 are also treated.