  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 nu =0.366(12) and
thus neither Gaussian (nu = 0.5) nor discontinuous (nu=0.25) type, indicating a
nontrivial continuum limit.
