Universal dynamics of independent critical relaxation modes

It is generally accepted that static critical phenomena in two dimensions fall into classes characterized by universal critical exponents and amplitude ratios. However, for dynamic critical phenomena the situation is much less clear, because exact and accurate numerical results are scarce. In this Letter, we show that relaxation modes of a class, parameterized by k, of two-dimensional Ising-like models with single-spin-flip dynamics have a universal exponent z and universal amplitude ratios of the corresponding relaxation times. At critically, tLiskd, the relaxation time of mode i of a system of size L, behaves as tLisk d. m k A i L z ,