Approach to the continuum limit of the quenched Hermitian Wilson-Dirac operator

We investigate the approach to the continuum limit of the spectrum of the Hermitian Wilson-Dirac operator in the supercritical mass region for pure gauge SU(2) and SU(3) backgrounds. For this we study the spectral flow of the Hermitian Wilson-Dirac operator in the range 0 less than or equal to m less than or equal to 2. We find that the spectrum has a gap for 0<m less than or equal to(1) and that the spectral density at zero, rho(0;m), is non-zero for m(1)less than or equal to m less than or equal to 2. We find that m(1)-->0 and, for m not equal 0, rho(0;m)-->0 (exponential in the lattice spacing) as one goes to the continuum limit. We also compute the topological susceptibility and the size distribution of the zero modes. The topological susceptibility scales well in the lattice spacing for both SU(2) and SU(3). The size distribution of the zero modes does not appear to show a peak at a physical scale. [S0556-2821(99)06613-8].