  We show that the functional renormalization group (FRG) allows for the
calculation of the probability distribution function of the sum of strongly
correlated random variables. On the example of the three-dimensional Ising
model at criticality and using the simplest implementation of the FRG, we
compute the probability distribution functions of the order parameter or
equivalently its logarithm, called the rate functions in large deviations
theory. We compute the entire family of universal scaling functions, obtained
in the limit where the system size $L$ and the correlation length of the
infinite system $\xi_{\infty}$ diverge, with the ratio $\zeta=L/\xi_{\infty}$
held fixed. It compares very accurately with numerical simulations.

Statistical Mechanics;High Energy Physics - Theory