Critical behaviour of the compact 3d U(1) gauge theory at finite temperature

TL;DR

This study investigates the critical behavior of the 3D compact U(1) lattice gauge theory at finite temperature, focusing on phase transition properties, critical indices, and string tension through numerical simulations.

Contribution

It provides new numerical insights into the critical indices and phase transition points of the 3D U(1) gauge theory, highlighting differences from previous assumptions and XY model predictions.

Findings

Critical index ν agrees with XY model value 1/2.

Determination of the infinite volume critical point differs from earlier pseudo-critical couplings.

Computed η index is larger than expected, indicating possible complex behavior.

Abstract

Critical properties of the compact three-dimensional U(1) lattice gauge theory are explored at finite temperatures. The critical point of the deconfinement phase transition, critical indices and the string tension are studied numerically on lattices with temporal extension N_t = 8 and spatial extension ranging from L = 32 to L = 256. The critical indices, which govern the behaviour across the deconfinement phase transition, are generally expected to coincide with the critical indices of the two-dimensional XY model. It is found that the determination of the infinite volume critical point differs 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 pseudocritical couplings agrees well with the value $\nu$ = 1/2 of the XY model. The computation of the index $\eta$ brings to a value larger than expected. The possible reasons for such behaviour are discussed.