Free energy distribution function of a random Ising ferromagnet
Abstract
We study the free energy distribution function of a weakly disordered Ising ferromagnet in terms of the Ddimensional random temperature GinzburgLandau Hamiltonian. It is shown that besides the usual Gaussian 'body' this distribution function exhibits nonGaussian 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 slower than the right one (for large positive values of the free energy). It is argued that at the critical point the free energy of the random Ising ferromagnet in dimensions D < 4 is described by a nontrivial universal distribution function which is nonselfaveraging.
 Publication:

Journal of Statistical Mechanics: Theory and Experiment
 Pub Date:
 May 2012
 DOI:
 10.1088/17425468/2012/05/P05027
 arXiv:
 arXiv:1204.1831
 Bibcode:
 2012JSMTE..05..027D
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Disordered Systems and Neural Networks
 EPrint:
 10 pages, 2 figures