New method of deriving high temperature expansions for the Heisenberg model

Andreas Hehn, Natalija van Well, Matthias Troyer

Jos Rogiers

Masahiro Shiroishi, Minoru Takahashi

Recently a new integral equation describing the thermodynamics of the 1D Heisenberg model was discovered by Takahashi. Using the integral equation we have succeeded in obtaining the high-temperature expansion of the specific heat and the magnetic susceptibility up to O[(J/T)(100)]. This is much higher than those obtained so far by the standard methods such as the linked-cluster algorithm. Our results will be useful to examine various approximation methods to extrapolate the high-temperature expansion to the low temperature region.

E. Praveczki

To avoid the difficulties with the usual type of (canonical) high-temperature series which arise when T<Tc and H=O, it is suggested that a high-temperature expansion be accomplished using the microcanonical ensembles of systems defined as involving only those states having values of the order parameter equal to the temperature-averaged one. The method is applied for the Ising and Heisenberg model utilising the molecular-field picture, and for the Heisenberg model using the spin-wave picture. In the latter case, the spin-wave energy is expanded according to the high-temperature parameter. It is shown that (m,m+1)-type Pade approximants are good at all temperatures. It is found that the longitudinal susceptibility chi L, diverges like H-1/2 at T<Tc; consequently, the critical exponent gamma ' no longer holds. A new critical exponent, gamma is defined as scaling the reduced susceptibility, chi 0=H1/2chi L. Deriving the scaling-law relating gamma with beta and delta , gamma is estimated as 0.18.

M. J. Škrinjaŕ, D. Kapor, Jovan P. Šetrajčić

David W. Wood