Critical couplings and string tensions via lattice matching of RG decimations

TL;DR

This paper introduces a simple lattice matching method using RG block transformations to accurately compute critical couplings and string tensions in SU(2) and SU(3) gauge theories, aligning well with Monte Carlo results.

Contribution

The paper presents a novel, inexpensive two-lattice matching technique with RG decimations for calculating critical couplings and string tensions in lattice gauge theories.

Findings

Critical couplings match Monte Carlo results within a few percent.

String tensions are accurately computed with this method.

The approach works over a wide range of lattice sizes.

Abstract

We calculate critical couplings and string tensions in SU(2) and SU(3) pure lattice gauge theory by a simple and inexpensive technique of two-lattice matching of RG block transformations. The transformations are potential moving decimations generating plaquette actions with large number of group characters and exhibit rapid approach to a unique renormalized trajectory. Fixing the critical coupling $\beta_c(N_\tau)$ at one value of temporal lattice length $N_\tau$ by MC simulation, the critical couplings for any other value of $N_\tau$ are then obtained by lattice matching of the block decimations. We obtain $\beta_c(N_\tau)$ values over the range $N_\tau = 3 - 32$ and find agreement with MC simulation results to within a few percent in all cases. A similar procedure allows the calculation of string tensions with similarly good agreement with MC data.