LOGARITHMIC TRIVIALITY OF SCALAR QUANTUM ELECTRODYNAMICS

Using finite size scaling and histogram methods we obtain results from lattice simulations indicating the logarithmic triviality of scalar quantum electrodynamics, even if the bare gauge coupling is large. Simulations of the noncompact formulation of the lattice Abelian Higgs model with fixed length scalar fields on L4 lattices with L ranging from 6 through 20 indicate a line of second-order critical points. Lengthy runs for each L produce specific-heat peaks which grow logarithmically with L and whose critical coupling shift with L picking out a correlation length exponent of 0.50(2) consistent with mean-field theory.