New Variant of the Fermionic Model on the Hierarchical Two-Dimensional Lattice

Abstract

We propose a generalization of 4-component fermionic model to a two-dimensional hierarchical lattice, in which the unit cell is represented by 4 vertices of a square. In this model the interaction between the spins in the vertices on the diagonal is different from the interaction between the spins in the vertices on the side of the square. We introduce new Gaussian fermionic field which is invariant under the block-spin renormalization group transformation (self-similar field). We describe this field in the Gibbsian form in the finite volume of the hierarchical lattice. We consider the non-Gaussian model in which the Gaussian part is given by the self-similar field and non-Gaussian part is given by the self-interaction. We show that the action of the renormalization group is local and is defined by the finite-dimensional superintegral.