$W$ : an alternative phenomenological coupling parameter for model systems

We introduce a parameter $W(\beta,L)= (\pi\,\langle |m| \rangle^2/\langle m^2 \rangle - 2)/(\pi-2)$ 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.