Free Energy Distribution Function of a Random Ising ferromagnet

TL;DR

This paper analyzes the distribution of free energy in a weakly disordered Ising ferromagnet, revealing non-Gaussian tails and a universal distribution at criticality, with implications for understanding disorder effects.

Contribution

It derives explicit asymptotic expressions for the non-Gaussian tails of the free energy distribution in disordered Ising ferromagnets, highlighting asymmetry and universality at criticality.

Findings

Distribution has non-Gaussian tails in both phases

Left tail decays slower than right tail

Universal non self-averaging distribution at critical point

Abstract

We study the free energy distribution function of weakly disordered Ising ferromagnet in terms of the D-dimensional random temperature Ginzburg-Landau Hamiltonian. It is shown that besides the usual Gaussian "body" this distribution function exhibits non-Gaussian tails both in the paramagnetic and in the ferromagnetic phases. Explicit asymptotic expressions for these tails are derived. It is demonstrated that the tails are strongly asymmetric: the left tail (for large negative values of the free energy) is much more slow than the right one (for large positive values of the free energy). It is argued that in the critical point the free energy of the random Ising ferromagnet in dimensions D<4 is described by a non-trivial universal distribution function being non self-averaging