Nonperturbative U(1) gauge theory at finite temperature

Abstract

For compact U(1) lattice gauge theory (LGT) we have performed a finite size scaling analysis on Nτ N 3 s lattices for Nτ fixed by extrapolating spatial volumes of size Ns ≤ 18 to Ns → ∞. Within the numerical accuracy of the thus obtained fits we find for Nτ = 4, 5 and 6 second order critical exponents, which exhibit no obvious Nτ 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.

Finite temperature and confinement along the extra dimensions studied on a five-dimensional U(1) lattice gauge model

“…Our findings contradict the ones of Ref. [12] that stipulate the existence of a Coulomb phase for L t ! 4 and !…”

“…A long-distance penetration of the external field is observed, accompanied by the renormalization of the magnetic charges due to the monopole currents. The case of 4D compact U(1) gauge theory at finite temperature was studied separately in [12,13]. The authors of Ref.…”

“…The authors of Ref. [12] reported a second-order phase transition to a Coulomb phase for L t ! 4, with critical exponents consistent with 3D Gaussian values and no obvious dependence on L t .…”

Direct numerical computation of disorder parameters

“…We have determined some relevant features of hi both in the confined and in the Coulomb phase. A careful analysis of its critical properties could help in clarifying the nature of the phase transition at zero as well as at finite temperature [33,34]: to that aim also a direct comparison with analogous order parameters developed for U1 [18,31] will be particularly useful.…”

Application of Biased Metropolis Algorithms: From protons to proteins

“…In a simulation one normally tunes the ratio between overrelaxation and other algorithms for optimal performance. For instance, in a recent study of U (1) gauge theory at finite temperature [6] on large volumes one BMA sweep was supplemented by two overrelaxation sweeps. The performance of the overrelaxation algorithm mixed with HBA and BMA was also studied for the case of the fundamental-adjoint SU (2) lattice gauge theory [3].…”