EXTRAPOLATION OF LATTICE GAUGE-THEORIES TO THE CONTINUUM LIMIT

The problem of extrapolating lattice gauge theories from the strong-coupling phase to the continuum critical point is studied for the Abelian [U(1)] and non-Abelian [SU(2)] theories in three (space-time) dimensions. A method is described for obtaining the asymptotic behavior, for large , of such thermodynamic quantities and correlation functions as the free energy and Wilson loop function. Certain general analyticity and positivity properties (in the complex plane) are shown to lead, after appropriate analytic remappings, to a Stieltjes property of these functions. Rigorous theorems then guarantee uniform and monotone convergence of the Padé approximants, with exact pointwise upper and lower bounds. The first three Padé approximants are computed for both the free energy and the Wilson function. For the free energy, we obtain satisfactory agreement with the asymptotic behavior computed by an explicit lattice calculation. The strong-coupling series for the Wilson function is found to be considerably more unstable in the lower-order terms correspondingly, convergence of the Padé approximants is found to be slower than in the free-energy case. It is suggested that higher-order calculations may allow a reasonably accurate determination of the string constant for the SU(2) theory. © 1979 The American Physical Society.