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

TL;DR

This paper provides exact high-temperature series expansions for the susceptibilities of the d-dimensional Ising model, analyzing how critical parameters depend on lattice dimensionality, and extends existing series for the critical temperature.

Contribution

It offers the first exact high-temperature expansions up to 20th order for susceptibilities in general dimension d, and significantly extends the series for the critical temperature.

Findings

Series coefficients calculated up to 20th order

Critical temperature series extended by more than double

Critical parameters depend on lattice dimensionality

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.