Nonperturbative U(1) gauge theory at finite temperature

For compact U(1) lattice gauge theory 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 nontrivial fixed point close to the 3d Gaussian emerges as one of the possible explanations.

Figure 1

Finite size dependence of the specific heat functions $C(\beta )$ on $N_{\tau }=6$ lattices.

Figure 2

Finite size dependence of the specific heat functions $C(\beta )$ on $N_{\tau }=N_s$ lattices.

Figure 3

Maxima of the specific heat.

Figure 4

Maxima of Polyakov loop susceptibilities.

Figure 5

Structure factors (7) for $N_{\tau }=6$.

Figure 6

Rescaled maxima of Polyakov loop susceptibilities.