Perfect Lattice Actions for the Gross-Neveu Model at large N

TL;DR

This paper constructs fixed point lattice actions for the Gross-Neveu model at large N, achieving a perfect action that eliminates cut-off effects and reproduces continuum spectra exactly, enhancing lattice field theory accuracy.

Contribution

It introduces a method to create perfect lattice actions for the Gross-Neveu model at large N, reducing discretization errors significantly.

Findings

Fermionic 1-particle energy spectrum matches continuum exactly

Cut-off effects in the chiral condensate are eliminated

Fixed point actions are constructed via renormalization group transformations

Abstract

Fixed point actions for free and interacting staggered lattice fermions are constructed by iterating renormalization group transformations. At large N the fixed point action for the Gross-Neveu model is a perfect action in the sense of Hasenfratz and Niedermayer, i.e. cut-off effects are completely eliminated. In particular, the fermionic 1-particle energy spectrum of the lattice theory is identical with the one of the continuum even for arbitrarily small correlation lengths. The cut-off effects of the chiral condensate are eliminated using a perfect operator. (The paper is stored as a ps-file containing both the text and 5 figures.)