Probability distribution of the order parameter for the three-dimensional Ising-model universality class: A high-precision Monte Carlo study

We study the probability distribution P(M) of the order parameter (average magnetization) M, for the finite-size systems at the critical point. The sy stems under consideration are the 3-dimensional Ising model on a simple cub ic lattice, and its 3-state generalization known to have remarkably small c orrections to scaling. Both models are studied in a cubic box with periodic boundary conditions. The model with reduced corrections to scaling makes i t possible to determine P(M) with unprecedented precision. We also obtain a simple, but remarkably accurate, approximate formula describing the univer sal shape of P(M).