Looking for the Logarithms in Four-Dimensional Nambu-Jona-Lasinio Models

TL;DR

This paper investigates triviality in four-dimensional Nambu-Jona-Lasinio models with discrete chiral symmetry, using large-N expansions and lattice simulations to identify logarithmic corrections and finite size effects.

Contribution

It demonstrates the presence of logarithmic corrections to scaling in the Nambu-Jona-Lasinio model and analyzes finite size effects, providing insights applicable to other field theories.

Findings

Logarithmic corrections to scaling are observed.

Finite size effects influence triviality analysis.

Differences between scalar and fermion field theories are discussed.

Abstract

We study the problem of triviality in the four dimensional Nambu-Jona-Lasinio model with discrete chiral symmetry using both large-N expansions and lattice simulations. We find that logarithmic corrections to scaling appear in the equation of state as predicted by the large-N expansion. The data from $16^4$ lattice simulations is sufficiently accurate to distinguish logarithmically trivial scaling from power law scaling. Simulations on different lattice sizes reveal an interesting interplay of finite size effects and triviality. We argue that such effects are qualitatively different for theories based on fundamental scalar rather than fermion fields. Several lessons learned here can be applied to simulations and analyses of more challenging field theories.