Dynamics And Thermodynamics Of Nonlinear Low Dimensional Magnetic And Electromagnetic Systems Microform

Results of a theoretical study of low-dimensional nonlinear systems are reported. One system is the isotropic Heisenberg ferromagnet with long range spin-spin interactions. The spin coupling parameter depends as the power law r-p on the distance r between spins. One-dimensional chains, two-dimensional square lattices, and two-layer films are considered as specific examples. The thermodynamic properties of these systems are investigated in a broad range of the parameter p using the Handscomb quantum Monte-Carlo method. The phase behavior and properties of the spin correlation functions are determined, and the critical indices and the temperature of the phase transition are calculated. Another system studied in this thesis is a dielectric multilayer structure with planar interfaces. In each of the layers the dielectric constant is generally a nonlinear function of the electric field. A new formalism is developed to study propagation of nonlinear optical waves in such a structure. The formalism is applied to a thin film sandwiched between two semi-infinite media and to an infinite periodic superlattice. Properties of the waves and the dispersion relations are investigated numerically.