Low Temperature Series Expansions of the Ising Model.

Sati McKenzie

Syh-Fu Lee, Keh-Ying Lin

Bernd Dammann, Joseph D. Reger

Lawrence E. Thomas, Yin Zhong

By conditioning on a subalgebra of observables, we develop low temperature expansions for certain quantum Ising models, which include transverse Ising models and anisotropic xy models. These expansions are majorized by the series for functions solving certain nonlinear partial differential equations. Convergence for the majorizing series follows from Cauchy–Kowalevski theory applied to the partial differential equations. The low temperature expansions imply long-range order.

Felix Lee, B. Westwański, Y. L. Wang

A linked-cluster expansion technique for spin systems has been used to obtain the free energy, the magnetization, and the susceptibility series for three Ising systems: (1) The Ising model; (2) The Blume-Capel model; and (3) The Blume-Emery-Griffiths (BEG) model. Each Hamiltonian is first divided into a single-ion potential and a term describing the interaction of the spin fluctuations. Only the latter is treated as perturbation in the series expansion. In the parametric phase our series reduces to the exact high-temperature series. However, in the ordered phase the same series can be used to study the low temperature behavior, such as the variation of the magnetization with temperature. The analysis of the eighth-order series for systems (1) and (2) show results in excellent agreement with the previous ones obtained from the high-temperature and low-temperature series. The series analysis for the BEG model shows quite different behavior from that predicted by the mean-field approximation.

H. Arisue, Kanehito Tabata