Critical behavior in many body systems

This work has been concentrated on a detailed study of low temperature (and high field) expansions for the simple Ising model. Methods were considered for their derivation and derived long series; these have been analyzed to provide evidence on critical indices. Also studied were the derivation of series expansions for the Ising model with spin S = 1/2 and the corresponding low temperature behavior. Also reported is a study of the configurational problem presented by the Potts model and the planar Potts model. The former model in particular has attracted particular attention recently in relation to the properties of liquid crystals. There is evidence that its behavior differs significantly from that of the Ising model and may in certain circumstances lead to a first order transition. Work has continued with a general program of tabulation of lattice constants for all standard two and three dimensional lattices. (Modified author abstract)