V Conclusion

[73.2.2.1] Our main conclusion in this paper is that the universal scaling function for the order parameter distribution at the critical point cannot be considered to be known from numerical simulations at present. [73.2.2.2] Our extrapolations indicate that current methods to estimate this quantity require system sizes that are beyond present day numerical resources even for the two-dimensional Ising model. [73.2.2.3] Our differential analysis shows that system sizes of at least are needed to reach the asymptotic regime at criticality. [73.2.2.4] All our findings indicate that convergence with system size is generally very slow. [73.2.2.5] For fixed boundary conditions this includes even the convergence of to zero far above the critical point.