Higher-order corrections for the quadratic Ising lattice susceptibility

Four terms in the expansion for the zero-field susceptibility of the quadratic Ising lattice at criticality are known exactly. We have computed three additional terms in this expansion by analyzing Nickel’s high-temperature series for this lattice with second-order homogeneous differential approximants and Padé techniques. These three terms are found to vary as ‖t${\Vert }^{1/4}$,t, and ‖t${\Vert }^{5/4}$ with t=1-$T_c$/T, and their respective coefficients are obtained to within 0.01% accuracy. It is shown that, if terms of the form ‖t${\Vert }^{1/4}$ln‖t‖ and ‖t${\Vert }^{5/4}$ln‖t‖ were present, their amplitudes would be less than ${10}^{\mathrm{-}5}$ of the amplitudes of the ‖t${\Vert }^{1/4}$ and ‖t${\Vert }^{5/4}$ terms, respectively. The results are in accord with the predictions of the renormalization group if irrelevant variables are neglected and indicate that, if singularities due to irrelevant variables are present, their associated exponents must exceed 2. The results are also used to predict the coefficients of the low-temperature series for this system. Agreement to as much as one part in ${10}^5$ with the known first eleven coefficients of this series is obtained.