UNIVERSAL ISING DYNAMICS IN 2 DIMENSIONS

We explore several dominant eigenvalues of the spectra of Markov matri ces governing the dynamics of models in the universality class of the two-dimensional Ising model. By means of a variational approximation, we determine autocorrelation times of progressively rapid relaxation m odes. The approximation of one eigenstate, associated with the slowest mode, is employed in a variance-reducing Monte-Carlo method. The resu lting correlation times, for which statistical errors exceed the syste matic errors associated with the variational approximation, are used f or a finite-size scaling analysis which corroborates universality of t he dynamic critical exponent z for three distinct Ising models on the square lattice. Tentative, variational results for subdominant states strongly suggest that the amplitudes of the divergent time scales asso ciated with different relaxation modes differ solely by metric factors , setting a single non-universal time scale for each model. A by-produ ct of our analysis is a highly accurate confirmation of static univers ality. (C) 1998 Elsevier Science B.V. All rights reserved.