Critical behavior of the compact 3d U(1) gauge theory on isotropic lattices

TL;DR

This paper investigates the critical behavior of the 3D U(1) lattice gauge theory at finite temperature, focusing on the phase transition, critical indices, and string tension, revealing discrepancies with expected universal values.

Contribution

It provides the first detailed numerical analysis of the critical indices and phase transition point in the 3D U(1) lattice gauge theory on isotropic lattices, highlighting deviations from universality.

Findings

Critical index ν matches XY model prediction (~1/2).

Critical index η shows significant deviation from universal value.

The infinite volume critical point differs from earlier pseudo-critical couplings.

Abstract

We report on the computation of the critical point of the deconfinement phase transition, critical indices and the string tension in the compact three dimensional U(1) lattice gauge theory at finite temperatures. The critical indices govern the behavior across the deconfinement phase transition in the pure gauge U(1) model and are generally expected to coincide with the critical indices of the two-dimensional XY model. We studied numerically the U(1) model for N_t=8 on lattices with spatial extension ranging from L=32 to L=256. Our determination of the infinite volume critical point on the lattice with N_t=8 differs substantially from the pseudo-critical coupling at L=32, found earlier in the literature and implicitly assumed as the onset value of the deconfined phase. The critical index $\nu$ computed from the scaling of the pseudo-critical couplings with the extension of the spatial lattice agrees well with the XY value $\nu$=1/2. On the other hand, the index $\eta$ shows large deviation from the expected universal value. The possible reasons of such behavior are discussed in details.