Universal free-energy distribution in the critical point of a random Ising ferromagnet

We discuss the non-self-averaging phenomena in the critical point of weakly disordered Ising ferromagnet. In terms of the renormalized replica Ginzburg-Landau Hamiltonian in dimensions $D<4$, we derive an explicit expression for the probability distribution function (PDF) of the critical free-energy fluctuations. In particular, using known fixed-point values for the renormalized coupling parameters, we obtain the universal curve for such PDF in the dimension $D=3$. It is demonstrated that this function is strongly asymmetric: its left tail is much slower than the right one.

Figure 1

Critical free energy distribution function of the disordered Ising ferromagnet in dimension $D=3$.