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)/hD/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.
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Dotsenko, V. Griffiths Singularity in the Random Ising Ferromagnet. J Stat Phys 122, 197–216 (2006). https://doi.org/10.1007/s10955-005-8079-6
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DOI: https://doi.org/10.1007/s10955-005-8079-6