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Critical finite-size scaling functions for the order parameter distributionof the two and three dimensional Ising model are investigated. Within arecently introduced classification theory of phase transitions, the universalpart of the critical finite-size scaling functions has been derived byemploying a scaling limit that differs from the traditional finite-size scalinglimit. In this paper the analytical predictions are compared with Monte Carlosimulations. We find good agreement between the analytical expression and thesimulation results. The agreement is consistent with the possibility that thefunctional form of the critical finite-size scaling function for the orderparameter distribution is determined uniquely by only a few universalparameters, most notably the equation of state exponent.Comment: 11 pages postscript, plus 2 separate postscript figures, all as  uuencoded gzipped tar file. To appear in J. Phys. A

Are critical finite-size scaling functions calculable from knowledge of an appropriate critical exponent?