Griffiths Singularity in the Random Ising Ferromagnet
Abstract
The explicit form of the Griffiths singularity in the random ferromagnetic Ising model in external magnetic field is derived. In terms of the continuous random temperature GinzburgLandau Hamiltonian it is shown that in the paramagnetic phase away from the critical point the free energy as the function of the external magnetic field h in the limit h → 0 has the essential singularity of the form exp [‑(const)/h^{D/3}] (where 1 < D < 4 is the space dimensionality). It is demonstrated that in terms of the replica formalism this contribution to the free energy comes due to nonperturbative replica instanton excitations.
 Publication:

Journal of Statistical Physics
 Pub Date:
 January 2006
 DOI:
 10.1007/s1095500580796
 arXiv:
 arXiv:condmat/0505233
 Bibcode:
 2006JSP...122..197D
 Keywords:

 Quenched disorder;
 instantons;
 replicas;
 meanfield;
 nonanalytic function;
 nonperturbative states;
 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Statistical Mechanics
 EPrint:
 14 pages, 3 figures