Susceptibility and fourth-field derivative of the spin-1/2Ising model for T>Tcand d=4

Abstract

THe authors investigate the spin-1/2 Ising model with nearest-neighbour interactions on the four-dimensional simple hypercubic lattice. High-temperature series expansions are studied for the zero-field susceptibility chi 0 and the fourth-field derivative of the free energy Xi 0(2) up to order nu 17. The series are analysed for singularities of the form t-1 mod 1nt mod p where t is the reduced temperature. For chi 0 it is found that p=0.33+or-0.07 when q=1, in good agreement with the prediction p=1/3, q=1 of renormalisation group theory. The critical temperature is estimated to be nu c-1=6.7315+or-0.0015. Results for chi 0(2) are more slowly convergent but are not inconsistent with the renormalisation group prediction p=1/3, q=4.