Yan V. Fyodorov - King's College London
Wednesday, April 19, 10:45AM EDT (Zoom meeting starts at 10:30 EDT)
Replica Symmetry Breaking transitions in the Large Deviations of spherical spin-glass ground state
We derive, within the replica formalism, a generalization of Crisanti-Sommers formula related to the large deviation function (LDF) for the rate-N atypical fluctuations of the intensive ground-state energy for a generic spherical spin-glass in the presence of a random magnetic field. We then analyse the ensuing LDF in much detail for the Replica Symmetric, single step Replica Symmetry Breaking (1-RSB) and Full Replica Symmetry Breaking (FRSB) situations. Our main qualitative conclusion is that the level of Replica Symmetry Breaking governing the LDF may be different from that for the typical ground state. In particular, it resolves the puzzling discrepancy between our earlier replica calculations for the simplest $p=2$ case and rigorous results by Dembo and Zeitouni which we are able to reproduce invoking 1-RSB pattern. The presentation will be based on a joint work with Bertrand Lacroix-A-Chez-Toine and Pierre Le Doussal.