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Griffiths singularity in the random Ising ferromagnet

Victor Dotsenko
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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 off-perturbative replica instanton excitations.

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Victor Dotsenko. 2005-05-10. Griffiths singularity in the random Ising ferromagnet. https://doi.org/10.1007/s10955-005-8079-6

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