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The mean spherical model in a random external field and the replica method

Authors:	J F Perez W F Wreszinski J L van Hemmen

Institution:	(1) Instituto de Física, Universidade de SÃo Paulo, SÃo Paulo, Brazil;(2) UniversitÄt Heidelberg, Sonderforschungsbereich 123, Heidelberg, West Germany

Abstract:	We provide a quick elementary solution of the mean spherical model in a random external field. This also allows an immediate proof of the self-averaging property of the free energy. We calculate the free energy by means of the replica method, i.e., for any (not necessarily integer) replica numbern, and show that when a phase transition occurs the limits $(\lim _{H \to 0_ + } \lim _{N \to \infty } )$ andn 0 are not interchangeable.

Keywords:	Mean spherical mode random external field self-averaging property critical dimension replica method thermodynamic convergence
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