A New Method of the High Temperature Series Expansion

Mathias Körner

Arisue, H, Fujiwara, T

New algorithm of the finite lattice method is presented to generate the high-temperature expansion series of the Ising model. It enables us to obtain much longer series in three dimensions when compared not only to the previous algorithm of the finite lattice method but also to the standard graphical method. It is applied to extend the high-temperature series of the simple cubic Ising model from beta^{26} to beta^{46} for the free energy and from beta^{25} to beta^{32} for the magnetic susceptibility.

Jos Rogiers, Turab Lookman, Donald D. Betts +1 more

Exact high temperature series expansions have been obtained for the free energy, the fluctuation of the transverse magnetization, and the fourth order fluctuation of the transverse magnetization of the spin [Formula: see text] model through degrees 13, 12, and 9, respectively, in the inverse temperature on one, two, three, and four dimensional lattices. A new method for identifying graphs and a new theorem for calculating vertical weights have been introduced in this work.

Donald D. Betts, D. Cuthiell, Michael Plischke

Ranjan K. Ghosh, Robert E. Shrock

We exhibit a new method for calculating high-and low-temperature series expansions for diagonal spin-spin correlation functions in the $d=2$ Ising model. The method makes use of a differential equation obeyed by these functions.

Sati McKenzie