The validity of hyperscaling in three dimensions for scalar spin systems

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Abstract
The exponents γ, ν and α are estimated from susceptibility and correlation length series for the bcc double-Gaussian and Klauder models, which interpolate, as a function of y, between the pure Gaussian model (at y = 0) and the pure spin 1/2 Ising model (at y = 1). Single-variable analysis reveals a value, yc (for each model), at which the leading, non-analytic corrections to pure power laws vanish, in accordance with expectations based on prior partial differential approximant analysis. The Hamiltonians of the two models display quasiuniversal features at these points. The corresponding exponent estimates are γ = 1.2395 ± 0.0004, ν = 0.632 ± 0.001 and α = 0.105 ± 0.007 : these imply dν - (2 - α) = 0.001 ± 0.010 and hence indicate the validity of hyperscaling. Apparent violations seen in the pure Ising model are attributable to small but significant nonanalytic corrections