TESTS OF THE CONTINUUM-LIMIT FOR THE SO(4) PRINCIPAL CHIRAL MODEL ANDTHE PREDICTION FOR DELTA((MS)OVER-BAR)

We investigate the continuum limit in SO(N) principal chiral models co ncentrating in detail on the SO(4) model and its covering group SU(2)x SU(2). We compute the mass gap in terms of Lambda MS and compare with the prediction of Hollowood of m/Lambda(MS)=3.8716. We use the finite- size scaling method of Luscher, Weisz, and Wolff to deduce m/Lambda(MS ) and find that for the SO(4) model the computed result of m/Lambda(MS )similar to 14 is in strong disagreement with theory but that a simila r analysis of the SU(2)xSU(2) model yields excellent agreement with th eory. We conjecture that for SO(4) violations of the finite-size scali ng assumption are severe for the values of the correlation length xi i nvestigated and that our attempts to extrapolate the results to zero l attice spacing, although plausible, are erroneous. Conversely, the fin ite-size scaling violations in the SU(2)xSU(2) simulation are consiste nt with perturbation theory and the computed beta function agrees well with the three-loop approximation for couplings evaluated at scales L /a less than or equal to xi, where xi is measured in units of the latt ice spacing a. We conjecture that lattice vortex artifacts in the SO(4 ) model are responsible for delaying the onset of the continuum limit until much larger correlation lengths are achieved notwithstanding the apparent onset of scaling. Results for the mass spectrum for SO(N), N =8,10 are given whose comparison with theory gives plausible support t o our ideas.