MICROCANONICAL RENORMALIZATION-GROUP SIMULATION OF ISING SYSTEMS

We report the results of a microcanonical simulation of the two- and three-dimensional Ising models at criticality. We also present a microcanonical algorithm that allows a simultaneous simulation of a lattice spin system at different energies, in our case the number of different energies is 32. The critical behavior of the systems was studied via a recently proposed microcanonical renormalization-group technique that yields independent estimates for the critical energy and the critical temperature, as well as for three critical exponents providing a direct test of hyperscaling. Our results in two dimensions are in good agreement with exact results. In three dimensions our quoted values are consistent with Monte Carlo estimates recently reported in the literature. We obtain u(c) = -0.991(1), T(c) = 4.5112(3), beta/nu = 0.541(1), nu = 0.630(3), and alpha = 0.109(1).