High-temperature series expansion for spin 1/2 xy-model in a magnetic-field

Jos Rogiers, Raf Dekeyser

J.T. Tsai, C. J. Elliott

Donald D. Betts, C. J. Elliott, M. Howard Lee

B. Bernu, C. Lhuillier

We explain how and why all thermodynamic properties of spin systems can be computed in one and two dimensions in the whole range of temperatures overcoming the divergence towards zero temperature of the standard high-temperature series expansions (HTEs). The method relies on an approximation of the entropy versus energy (microcanonical potential function) on the whole range of energies. The success is related to the intrinsic physical constraints on the entropy function and a careful treatment of the boundary behaviors. This method is benchmarked against two one-dimensional solvable models: the Ising model in longitudinal field and the XY model in a transverse field. With ten terms in the HTE, we find a spin susceptibility within a few percent of the exact results over the entire range of temperatures. The method is then applied to two two-dimensional models: the supposedly gapped Heisenberg model and the J(1)-J(2)-J(d) model on the kagome lattice.

Andreas Hehn, Natalija van Well, Matthias Troyer

Kazuo Torii Nakamura, Tomohei Sasada

The exact analytical forms of the low-temperature free energy, and longitudinal and transverse correlation functions are obtained for the continuum model of the classical one-dimensional Heisenberg ferromagnet in a magnetic field. The calculated results show a few leading terms in series expansion with respect to the reduced temperature. It is also pointed out that the low-temperature free energy can not be identified with its counterpart for the XY model in a magnetic field.