Le Journal de Physique Colloques

LOW TEMPERATURE CRITICAL BEHAVIOUR OF THE ISING MODEL OF FERROMAGNETISM

Anthony John Guttmann, Cyril Domb, P F Fox

Published Feb 1, 1971• 0 citations

Abstract

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.

DOI: 10.1051/jphyscol:19711121

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