Universality of the gauge-ball spectrum of the four-dimensional pure U(1) gauge theory

Abstract

We continue numerical studies of the spectrum of the pure U(1) lattice gauge theory in the confinement phase, initiated in our previous work. Using the extended Wilson action $ S = -\sum_P [β\cos(Θ_P) + γ\cos(2Θ_P)] $ we address the question of universality of the phase transition line in the ($β,γ$) plane between the confinement and the Coulomb phases. Our present results at $γ= -0.5$ for the gauge-ball spectrum are fully consistent with the previous results obtained at $γ= -0.2$. Again, two different correlation length exponents, $ν_{ng} = 0.35(3)$ and $ν_{g} = 0.49(7)$, are obtained in different channels. We also confirm the stability of the values of these exponents with respect to the variation of the distance from the critical point at which they are determined. These results further demonstrate universal critical behaviour of the model at least up to correlation lengths of 4 lattice spacings when the phase transition is approached in some interval at $γ\leq -0.2$.