Griffiths singularity in the random Ising ferromagnet

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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 [-(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 off-perturbative replica instanton excitations.