Generation of low tehmperature series for Ising models with nearest and next nearest neighbor interactions

Abstract

We have generalized the code method of Sykes et al. and applied it to the Ising model with nearest and next nearest neighbor interactions. On the bcc lattice, we have obtained the first seven low temperature polynomials for arbitrary sign of the interactions. Special cases of this model are the Ising ferromagnet and the Ising antiferromagnet with next nearest neighbor ferromagnetic interactions. The latter system exhibits a tricritical point which we plan to study using our low temperature data and high temperature series to be obtained in the future.