Static quark potential and string tension for compact U(1) in (2+1) dimensions

TL;DR

This study investigates the static quark potential and string tension in (2+1)D compact U(1) lattice gauge theory using Monte Carlo simulations, revealing scaling behavior and asymptotic limits.

Contribution

It provides new estimates of the string tension and explores the scaling and asymptotic behavior in anisotropic lattice formulations of compact U(1) gauge theory.

Findings

Evidence of scaling in string tension for 1.4142 <= beta <= 2.5

Asymptotic behavior of K sqrt(beta) = e^(-2.494 beta + 2.29)

Extrapolations to the Hamiltonian limit and comparison with previous methods

Abstract

Compact U(1) lattice gauge theory in (2+1) dimensions is studied on anisotropic lattices using Standard Path Integral Monte Carlo techniques. We extract the static quark potential and the string tension from 1.0 <= Dtau <= 0.333 simulations at 1.0 <= beta <= 3.0. Estimating the actual value of the renormalization constant, (c = 44), we observe the evidence of scaling in the string tension for 1.4142 <= beta <= 2.5; with the asymptotic behaviour in the large-beta limit given by K sqrt(beta) = e^(-2.494 beta +2.29). Extrapolations are made to the extreme anisotropic or "Hamiltonian" limit, and comparisons are made with previous estimates obtained by various other methods in the Hamiltonian formulation.