On the validity of the replica method and its application to Ising chain in random field
Classical spin models in the presence of random interactions or external fields are considered. A general argument shows that the normal (non-Parisi-type) replica-trick is bound to yield the correct free energy provided that this latter is an analytic function of the strength ε of the random variables. As an illustration, the free energy of the one-dimensional Ising model in random external field is calculated up to sixth order in e by direct computation and also by the replica method, and the coincidence of the two results is demonstrated.
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