Universal Dynamics of Independent Critical Relaxation Modes

M. P. Nightingale; H. W. J. Blöte

doi:10.1103/PhysRevLett.80.1007

Universal Dynamics of Independent Critical Relaxation Modes

M. P. Nightingale and H. W. J. Blöte

Phys. Rev. Lett. 80, 1007 – Published 2 February 1998

Abstract

We obtain the relaxation times of several, progressively rapid, independent modes of three models in a two-dimensional Ising universality class. Their size dependence can be described by one single dynamic exponent and universal amplitude ratios. This analysis is based on variational approximations of the eigenstates of the Markov matrix describing heat-bath, single-spin-flip dynamics. Monte Carlo computation of the corresponding autocorrelations and cross correlations, in which the variational error is systematically reduced, yields eigenvalues and the associated relaxation times with considerably higher statistical accuracy than is the case for traditional correlations.

Received 7 August 1997

DOI:https://doi.org/10.1103/PhysRevLett.80.1007

Authors & Affiliations

M. P. Nightingale

Department of Physics, University of Rhode Island, Kingston, Rhode Island 02881

H. W. J. Blöte

Department of Applied Physics, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands
and Lorentz Institute, Leiden University, P.O. Box 9506, 2300 RA Leiden, The Netherlands