Low temperature critical behaviour of the spin 1 Ising model

Alvaro Caramico D’Auria, L. De Cesare, Ileana Rabuffo

Alvaro CaramicoD'Auria, Luigi DeCesare, Ileana Rabuffo

P F Fox, Anthony John Guttmann

Low temperature series expansions for the Ising model with spin S=1 and S= 3 / 2 are derived for a number of two and three dimensional lattices. For each spin-lattice combination the critical point is estimated, and then the critical exponents beta and gamma ' with their corresponding critical amplitudes are also estimated. The principal conclusion is that there is no compelling evidence to suggest that the above critical exponents differ from their S= 1 / 2 values.

Rajiv R. P. Singh

Anthony John Guttmann, Cyril Domb, P F Fox

Low temperature series expansions for the spin S = 1 Ising model on various two and three dimensional lattices have been generated. By extrapolation of these series, it is found that the critical exponents β, γ' and δ appear to be the same as for the spin S = 1/2 Ising model. For the spin S = 1/2 Ising model, we have found that the class of configurations represented by Cayley trees make a significant contribution to the low temperature series coefficients. In particular, we find that the distribution of singularities within the disk | u | ≤ |uc |(uc = exp[- 4 J/kTc], Tc is the critical temperature) is well represented by including only the Cayley trees in the partition function.

N. Hachem, A. Ezzaime, M. El Bouziani