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We present a numerical study of the order-parameter probability densityfunction (PDF) of the square Ising model for lattices with linear sizes$L=80-140$. A recent efficient entropic sampling scheme, combining theWang-Landau and broad histogram methods and based on the high-levels of theWang-Landau process in dominant energy subspaces is employed. We find that forlarge lattices there exists a stable window of the scaled order-parameter inwhich the full ansatz including the pre-exponential factor for the tail regimeof the universal PDF is well obeyed. This window is used to estimate theequation of state exponent and to observe the behavior of the universalconstants implicit in the functional form of the universal PDF. The probabilitydensities are used to estimate the universal Privman-Fisher coefficient and toinvestigate whether one could obtain reliable estimates of the universalconstants controlling the asymptotic behavior of the tail regime.

Universal features and tail analysis of the order-parameter distribution of the two-dimensional Ising model: An entropic sampling Monte Carlo study