Universal Dynamics of Independent Critical Relaxation Modes

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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.