On the REM approximation of TAP free energies
- The free energy of TAP-solutions for the SK-model of mean field spin glasses can be expressed as a nonlinear functional of local terms: we exploit this feature in order to contrive abstract REM-like models which we then solve by a classical large deviations treatment. This allows to identify the origin of the physically unsettling quadratic (in the inverse of temperature) correction to the Parisi free energy for the SK-model, and formalizes the true cavity dynamics which acts on TAP-space, i.e. on the space of TAP-solutions. From a non-spin glass point of view, this work is the first in a series of refinements which addresses the stability of hierarchical structures in models of evolving populations.
| Author: | Nicola KistlerORCiDGND, Marius Alexander SchmidtGND, Giulia SebastianiGND |
|---|---|
| URN: | urn:nbn:de:hebis:30:3-856770 |
| DOI: | https://doi.org/10.1088/1751-8121/acdf30 |
| ISSN: | 1751-8113 |
| ArXiv Id: | http://arxiv.org/abs/2212.11718 |
| Parent Title (English): | Journal of Physics. A. Mathematical and Theoretical |
| Publisher: | IOP Publishing |
| Place of publication: | Bristol |
| Document Type: | Article |
| Language: | English |
| Date of Publication (online): | 2023/06/30 |
| Date of first Publication: | 2023/06/30 |
| Publishing Institution: | Universitätsbibliothek Johann Christian Senckenberg |
| Granting Institution: | Johann Wolfgang Goethe-Universität |
| Release Date: | 2024/06/13 |
| Volume: | 56 |
| Issue: | 29, 294001 |
| Article Number: | 294001 |
| Page Number: | 30 |
| Institutes: | Informatik und Mathematik / Mathematik |
| Physik / Physik | |
| Informatik und Mathematik / Informatik | |
| Wissenschaftliche Zentren und koordinierte Programme / Frankfurt Institute for Advanced Studies (FIAS) | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Sammlungen: | Universitätspublikationen |
| Licence (German): |  Creative Commons - Namensnennung 4.0 |
