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 number”n, and show that when a phase transition occurs the limits\((\lim _{H \to 0_ + } \lim _{N \to \infty } )\) andn → 0 are not interchangeable.
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