TY - THES A1 - Sebastiani, Giulia T1 - From Parisi to Boltzmann : on an abstract class of mean field spin glasses N2 - During my initial days here in Frankfurt, in October 2020 amidst the pandemic crisis, all my notes revolved around three articles by Bolthausen and Kistler, which now form the starting point of this work. The ones introduced by Bolthausen and Kistler are abstract mean field spin glass models, reminiscent of Derrida’s Generalized Random Energy Model (GREM), which generalize the GREM while remaining rigorously solvable through large deviations methods and within a classical Boltzmann-Gibbs formalism. This allows to establish, by means of a second moment method, the associated free energy at the thermodynamic limit as an orthodox, infinite-dimensional, Boltzmann-Gibbs variational principle. Dual Parisi formulas for the limiting free energy associated with these Hamiltonians hold, and are revealed to be the finite-dimensional (”collapsed”) versions of the classical, infinite-dimensional Boltzmann-Gibbs principles. In the 2nd chapter of this thesis, we uncover the hidden yet essential connection between real-world spin glasses, like the Sherrington-Kirkpatrick (SK) model and the random energy models. The crucial missing element is that of TAP-free energies: integrating it with the framework introduced by Bolthausen and Kistler results in a correction to the Parisi formula for the free energy, which brings it much, much closer to the ”true” Parisi solution for the SK-model. In other words, we can identify the principles that transform the classical Boltzmann-Gibbs maximization into the unorthodox (and puzzling) Parisi minimization. This arguably stands as the primary achievement of this work. Y1 - 2024 UR - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/85838 UR - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-858380 N1 - Kumulative Dissertation - enthält die Verlagsversionen (Versions of Record) der folgenden Artikel: Kistler, Nicola; Sebastiani, Giulia (2021): On a nonhierarchiacal generalization of the Perceptron GREM. Stochastic Processes and their Applications 2023, Vol 163, September 2023, Seite 1-24, ISSN 0304-4149, DOI 10.1016/j.spa.2023.05.008 Kistler, Nicola; Schmidt, Marius A.; Sebastiani, Giulia (2023): On the REM approximation of TAP free energies. Journal of Physics A, Mathematical and Theoretical 2023, Vol 56, 294001, ISSN 1751-8121, DOI 10.1088/1751-8121/acdf30 Die Manuskriptversion des folgenden Artikels: Sebastiani, Giulia, Schmidt, Marius Alexander: On the GREM approximation of tap free engines. 2024, DOI 10.48550/arXiv.2401.13507 CY - Frankfurt am Main ER -