Scaling in the Positive Plaquette Model and Universality in SU(2) Lattice Gauge Theory

TL;DR

This paper examines the positive plaquette model in SU(2) lattice gauge theory, demonstrating that removing negative plaquettes does not alter the universality class but affects the approach to the continuum limit.

Contribution

It shows that the positive plaquette model shares the same universality class as the standard Wilson formulation despite differences in the beta-function behavior.

Findings

Positive plaquette model and Wilson formulation have the same continuum limit.

The beta-function differs, lacking a dip in the positive plaquette model.

Physical quantities like critical temperature and glueball masses are consistent across models.

Abstract

We investigate universality, scaling, the beta-function and the topological charge in the positive plaquette model for SU(2) lattice gauge theory. Comparing physical quantities, like the critical temperature, the string tension, glueball masses, and their ratios, we explore the effect of a complete suppression of a certain lattice artifact, namely the negative plaquettes, for SU(2) lattice gauge theory. Our result is that this modification does not change the continuum limit, i.e., the universality class. The positive plaquette model and the standard Wilson formulation describe the same physical situation. The approach to the continuum limit given by the beta-function in terms of the bare lattice coupling, however, is rather different: the beta-function of the positive plaquette model does not show a dip like the model with standard Wilson action.