期刊
JOURNAL OF STATISTICAL PHYSICS
卷 122, 期 2, 页码 197-216出版社
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10955-005-8079-6
关键词
quenched disorder; instantons; replicas; ruean-field; non-analytic function; non-perturbative states
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 ill 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.
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