Analysis of coherent anomalies, scaling exponent and confluent singularities for spin-S Ising model on cubic nets

The zero-field high temperature static susceptibility series of the spin-S nearest-neighbour Ising model on simple cubic (SC), body-centred cubic (BCC) and face-centred cubic (FCC) lattices is thoroughly analysed by means of a power series coherent anomaly method (CAM). Our analysis revealed that the ten-term high-temperature susceptibility series is consistent with the universal value of the scaling exponent γ = 54 for all S and for all cubic nets, provided that (i) a single confluent correction of the form Δ∗ ≅ o.44 is inserted for FCC lattice and for all spins except S = 12 and (ii) two confluent corrections Δo∗and Δ3∗ are inserted for SC and BCC lattices covering all spins except the spin-12 case. For S = 12, the results obtained for all lattices demonstrate the non-existence (except for the SC lattice where Δo∗ ≠ 0, Δe∗ = 0) of confluent correction in agreement with the observation of earlier authors. The variation Tc∗ for all lattices and for all spin is also analysed quantitatively.