Phys. Rev. B 74, 054410 (2006) [9 pages]Hierarchical solutions of the Sherrington-Kirkpatrick model: Exact asymptotic behavior near the critical temperatureReceived 20 December 2005; published 8 August 2006 We analyze the replica-symmetry-breaking construction in the Sherrington-Kirkpatrick model of a spin glass. We present a general scheme for deriving an exact asymptotic behavior near the critical temperature of the solution with an arbitrary number of discrete hierarchies of the broken replica symmetry. We show that all solutions with finitely many hierarchies are unstable and only the scheme with infinitely many hierarchies becomes marginally stable. We show how the solutions from the discrete replica-symmetry-breaking scheme go over to the continuous one with increasing number of hierarchies. © 2006 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevB.74.054410
DOI:
10.1103/PhysRevB.74.054410
PACS:
64.60.Cn, 75.50.Lk
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