On hyperscaling in the Ising model in three dimensions

The spin-¹/₂ Ising model high-temperature series are re-examined by an analysis that parallels the method used to analyse the continuum phi ⁴ spin model. Results of the Ising model in three dimensions do not agree with results in the literature based on more conventional methods of analysis. The authors cannot decide using only the series terms presently available, which of the methods is to be preferred. They conclude that previous error assessments are unduly optimistic and that the three-dimensional, spin-¹/₂, Ising model may satisfy hyperscaling in agreement with the continuum results. An attempt is made to estimate the number of additional high-temperature series terms necessary to resolve the hyperscaling question.