W: an alternative phenomenological coupling parameter for model systems

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We introduce a parameter W(β,L)= (π |m| ²/ m² - 2)/(π-2) which like the kurtosis (Binder cumulant) is a phenomenological coupling characteristic of the shape of the distribution p(m) of the order parameter m. To demonstrate the use of the parameter we analyze extensive numerical data obtained from density of states measurements on the canonical simple cubic spin-1/2 Ising ferromagnet, for sizes L=4 to L=256. Using the W-parameter accurate estimates are obtained for the critical inverse temperature βc = 0.2216541(2), and for the thermal exponent ν= 0.6308(4). In this system at least, corrections to finite size scaling are significantly weaker for the W-parameter than for the Binder cumulant.