Crystal field effect in an Ising model

Abstract

The crystal field effect has been studied in the linear Ising model which can be solved exactly. For spins S= 1/2 , 1, (3)/(2) it is easy to diagonalize the transfer matrix analytically, but for spins S> (3)/(2) , the transfer matrices are diagonalized numerically. The numerical results are accurate to seven decimal places and can be treated as exact for all practical purposes. Crystal field has no effect on spin- 1/2 systems, its effect has been studied in systems with spins S> (1)/(2) . The ferromagnetic as well as the antiferromagnetic sysceptibilities have been computed for the systems with and without the crystal field. It has been found that, for small crystal fields, the susceptibility behavior is not much different from that in the absence of crystal field. But for large crystal fields, not only the antiferromagnetic susceptibilities but the ferromagnetic susceptibilities also start showing maxima which appear for integer spins only.