On the corrections to scaling in three-dimensional Ising models

The leading correction-to-scaling amplitudes for the spin-1/2, nearest-neighbor sc, bcc, and fee Ising models are considered with the particular aim of determining their signs. On the basis of previous two-variable series analyses by Chen, Fisher, and Nickel and renormalization group=4–d expansions, it is concluded that the correction amplitudes for the susceptibility, correlation length, specific heat, and spontaneous magnetization arenegative for all three lattices. Thus, for example, the effective exponent_eff(T) asymptotically approaches the true susceptibility exponent fromabove. Other earlier and more recent high-temperature series and field-theoretic analyses are seen to be consistent with this result. However, the usual nonasymptotic, perturbative field-theoretic approaches are essentially committed to positive correction amplitudes. The question of the signs therefore relates directly to the applicability of these non-asymptotic field-theoretic calculations to three-dimensional Ising models as well as to different experimental systems.