Compact U(1) in 2+1 dimensions: The finite-lattice Hamiltonian approach

We have studied the mass spectrum and phase structure of compact electrodynamics in $D=2+1\mathrm{}$ dimensions using the finite-lattice Hamiltonian approach. The numerical results are generally comparable to, but not significantly better than, available strong-coupling series results. Evidence for roughening of the "on-axis" string is found at $g^2=e^{2}a\simeq 1.5$ while the vacuum and glueball sectors of the theory are smooth for all attainable $g^2(\gtrsim 0.08)$. Comparisons with results from applying weak-coupling approximations to the theory are also presented.