High-temperature dynamics of classical spin systems
The high-temperature dynamics of various model systems of interacting classical spins has been studied by three different calculational techniques: (i) exact analysis, (ii) the recursion method, (iii) computer simulations. The dynamics of the classical XXZ model with uniform interaction is nonlinear for two and more spins (N > 2) and nonintegrable for N > 3. The nonlinearities disappear in the thermodynamic limit N [yields] [infinity], and the spin autocorrelation functions decay algebraically or Gaussian, depending on the spin component and the type and amount of uniaxial anisotropy. The classical two-sublattice XYZ model with uniform inter-sublattice interaction and zero intra-sublattice interaction is another integrable model for which dynamical spin correlation functions are calculated exactly. A numerical implementation of the recursion method is used for the investigation of the equivalent-neighbor XYZ model. At T = [infinity], the dynamical behavior is categorized into four different universality classes according to the decay law of the spectral densities at high frequencies. That decay law governs the growth rate of the sequence of recurrents which determine the relaxation function in the continued-fraction representation. These universality classes may serve as prototypes for a classification of the dynamics of classical and quantum many-body systems. The dynamics of some one-dimensional classical spin models with short-range interaction is investigated by means of computer simulations. This simulation study provides evidence that spin diffusion in the classical Heisenberg chain is anomalous. The exponential instability of the numerically integrated phase-space trajectories transforms the deterministic transport of spin fluctuations into a computationally generated stochastic process in which the global conservation laws are still satisfied. This may cause a crossover from anomalous spin diffusion to normal spin diffusion at some characteristic time lag.
- Research Organization:
- Rhode Island Univ., Kingston, RI (United States)
- OSTI ID:
- 7112675
- Resource Relation:
- Other Information: Thesis (Ph.D.)
- Country of Publication:
- United States
- Language:
- English
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