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We analyze the replica-symmetry-breaking construction in theSherrington-Kirkpatrick model of a spin glass. We present a general scheme forderiving an exact asymptotic behavior near the critical temperature of thesolution with an arbitrary number of discrete hierarchies of the broken replicasymmetry. We show that all solutions with finite-many hierarchies are unstableand only the scheme with infinite-many hierarchies becomes marginally stable.We show how the solutions from the discrete replica-symmetry-breaking scheme goover to the continuous one with increasing the number of hierarchies.Comment: REVTeX4, 11 pages, no figure

Hierarchical solutions of the Sherrington-Kirkpatrick model: Exact asymptotic behavior near the critical temperature