Perfect Lattice Actions for the Gross-Neveu Model

TL;DR

This paper analytically constructs perfect lattice actions for the Gross-Neveu model, eliminating cut-off artifacts and restoring symmetries, thus providing an exact lattice representation at finite correlation length.

Contribution

It presents the first analytic construction of an exactly perfect lattice action for the Gross-Neveu model at finite correlation length.

Findings

Elimination of cut-off artifacts in the large N limit

Exact matching of the energy spectrum with the continuum

Restoration of translation and rotation symmetries in observables

Abstract

We apply the method of Hasenfratz and Niedermayer to analytically construct perfect lattice actions for the Gross--Neveu model. In the large $N$ limit these actions display an exactly perfect scaling, i.e. cut-off artifacts are completely eliminated even at arbitrarily short correlation length. Also the energy spectrum coincides with the spectrum in the continuum and continuous translation and rotation symmetries are restored in physical observables. This is the first (analytic) construction of an exactly perfect lattice action at finite correlation length.