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 Ginzburg-Landau 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 non-perturbative replica instanton excitations.
- Publication:
-
Journal of Statistical Physics
- Pub Date:
- January 2006
- DOI:
- 10.1007/s10955-005-8079-6
- arXiv:
- arXiv:cond-mat/0505233
- Bibcode:
- 2006JSP...122..197D
- Keywords:
-
- Quenched disorder;
- instantons;
- replicas;
- mean-field;
- non-analytic function;
- non-perturbative states;
- Condensed Matter - Disordered Systems and Neural Networks;
- Condensed Matter - Statistical Mechanics
- E-Print:
- 14 pages, 3 figures