Non-Perturbative U(1) Gauge Theory at Finite Temperature

TL;DR

This study investigates the phase transition behavior of compact U(1) lattice gauge theory at finite temperature, revealing critical exponents consistent with a 3d Gaussian fixed point, suggesting the presence of a potentially new non-trivial fixed point.

Contribution

The paper provides a finite size scaling analysis of U(1) lattice gauge theory at finite temperature, identifying critical exponents that challenge existing universality class expectations.

Findings

Critical exponents are consistent with 3d Gaussian values.

No significant dependence of exponents on N_tau.

Results suggest a possible new non-trivial fixed point.

Abstract

For compact U(1) lattice gauge theory (LGT) we have performed a finite size scaling analysis on $N_{\tau} N_s^3$ lattices for $N_{\tau}$ fixed by extrapolating spatial volumes of size $N_s\le 18$ to $N_s\to\infty$. Within the numerical accuracy of the thus obtained fits we find for $N_{\tau}=4$, 5 and~6 second order critical exponents, which exhibit no obvious $N_{\tau}$ dependence. The exponents are consistent with 3d Gaussian values, but not with either first order transitions or the universality class of the 3d XY model. As the 3d Gaussian fixed point is known to be unstable, the scenario of a yet unidentified non-trivial fixed point close to the 3d Gaussian emerges as one of the possible explanations.