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

TL;DR

This paper derives a universal probability distribution for free-energy fluctuations at the critical point of a disordered 3D Ising ferromagnet, revealing strong asymmetry in the distribution's tails.

Contribution

It provides an explicit, universal PDF for critical free-energy fluctuations using renormalized replica Ginzburg-Landau theory in dimensions below four.

Findings

The PDF is strongly asymmetric with a slow-decaying left tail.

The universal curve is explicitly calculated for D=3.

The results highlight non-self-averaging phenomena at criticality.

Abstract

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.