The high-temperature expansions of the higher susceptibilities for the Ising model in general dimension d

Abstract

The high-temperature expansion coefficients of the ordinary and the higher susceptibilities of the spin-1/2 nearest-neighbor Ising model are calculated exactly up to the 20th order for a general d-dimensional (hyper)-simple-cubical lattice. These series are analyzed to study the dependence of critical parameters on the lattice dimensionality. Using the general $d$ expression of the ordinary susceptibility, we have more than doubled the length of the existing series expansion of the critical temperature in powers of 1/d.