Alternative phenomenological coupling parameter for finite-size analysis of numerical data at criticality

We introduce a parameter W(beta,L) =(pi (2)/< m(2)>- 2/(pi-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 beta(c)=0.2216541(2), and for the thermal exponent nu=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.