ISSN:
1089-7550
Source:
AIP Digital Archive
Topics:
Physics
Notes:
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 asΦ0(large-closed-square)ω(large-closed-square) ∼exp(large-closed-square) − ω2(large-closed-square)λ(large-closed-square), 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.350013
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