Universality classes of dynamical behavior (abstract)
Date of Original Version
In studies of dynamic correlation functions the focus is, in general, on their long-time asymptotic behavior and the singularity structure of the associated spectral densities. It turns out that the analysis of the same dynamic correlation functions from a quite different perspective is equally useful and revealing. The focus of our study is on the properties of spectral densities at high frequencies, specifically their decay law, expressible asΦ0large-closed-square signωlarge-closed-square sign ∼explarge-closed-square sign - ω 2large-closed-square signλlarge-closed-square sign, in terms of a characteristic exponent λ. That decay law governs the growth rate of the sequence of recurrents which determine the relaxation function in the continued-fraction representation. The value of λ contains valuable information on the underlying dynamical processes taking place in the system, which, in some sense, is complementary to that inferred from the singularity structure of spectral densities. A detailed study of the dynamics of various quantum and classical spin models has prompted us to introduce the concept of "universality class" for a classification of dynamical behavior on the basis of the characteristic exponent λ. For the equivalent-neighbor XYZ model1 we are able to demonstrate four different prototype universality classes: λ=0 (compact support), λ=1 (Gaussian decay), λ=2 (exponential decay), λ=3 (stretched exponential decay), which can be interpreted in terms of basic notions of classical dynamics. Finally, we present the exact T=∞ dynamic correlation functions for a two-sublattice Heisenberg antiferromagnet with uniform intersublattice interaction and zero intrasublattice interaction.
Journal of Applied Physics
Liu, Jian Min, and Gerhard Müller. "Universality classes of dynamical behavior (abstract)." Journal of Applied Physics 70, 10 (1991): 6187. doi:10.1063/1.350013.