We analyze the replica-symmetry-breaking (RSB) construction in the Sherrington - Kirkpatrick (SK) model and in the p-state Potts glass for p ≤ 4. We present a general scheme for deriving an asymptotic solution with an arbitrary number of discrete hierarchies of broken replica symmetry near the critical temperature for both models, and close to the de Almeida- Thouless instability line in the SK model. We show that in the SK model all solutions with finite many hierarchies are unstable and only the scheme with infinite many hierarchies becomes marginally stable in the spin-glass phase. For the Potts glass, we find, moreover, an one-step RSB solution which co- exists with the infinite RSB solution for p > p∗ ≈ 2.82. The former solution is locally stable but has lower free energy than the latter which is marginally stable and has the highest free energy. 1
| Identifer | oai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:327199 |
| Date | January 2013 |
| Creators | Klíč, Antonín |
| Contributors | Janiš, Václav, Zahradník, Miloš, Zdeborová, Lenka |
| Source Sets | Czech ETDs |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/doctoralThesis |
| Rights | info:eu-repo/semantics/restrictedAccess |
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