U(1) gauge theory with Villain action on spherical lattices

We have studied the U(1) gauge field theory with Villain (periodic Gaussian) action on spherelike lattices. The effective size of the systems studied ranges from 6 to 16. We do not observe any 2-state signal in the distribution function of the plaquette expectation value at the deconfining phase transition. The observed finite-size scaling behavior is consistent with a second order phase transition. The obtained value of the critical exponent is ν = 0.366(12) and thus neither Gaussian (ν = 0.5) nor discontinuous (ν = 0.25) type, indicating a nontrivial continuum limit.