Renormalization of a hierarchical fermion model in two dimensions

Abstract

Fermion fields on a lattice are easier to renormalize then Boson fields because the former do not have an infinite range of possible values. This becomes particularly transparent in a hierarchical model since the interaction stays strictly local in renormalizing such a model. The model considered here is obtained by dividing a square lattice into blocks, blocks of blocks and so forth at each level or scale. The blocks at the ℓ-th level will contain 2^2ℓ lattice sites. The ‘kinetic part’ of the action is then given by $\langle \overline \psi ,C^{ - 1} \psi \rangle$where C is the hierarchical covariance.