The free energy limit of the SYK model at high temperature
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913087257313280 |
|---|---|
| author | Gamarnik, David Pernice, Francisco Schmidhuber, Alexander Zlokapa, Alexander |
| author_facet | Gamarnik, David Pernice, Francisco Schmidhuber, Alexander Zlokapa, Alexander |
| contents | The Sachdev-Ye-Kitaev (SYK) model is a disordered quantum mean-field model studied in condensed matter physics and the holographic theory of black holes. Its structural properties can be derived heuristically using a combination of the replica method and path integration techniques. Analyzing it mathematically rigorously, however, turned out to be notoriously difficult, even for basic questions such as computing the annealed free energy.
In this paper we rigorously compute the free energy limit (annealed and quenched) for this model at high enough but constant temperature. Our results are in numerical agreement with the results derived by physics methods. Remarkably, though, our method of proof is novel and is different from the physics approach. It is based on (a) the theory of the component structure of sparse random graphs and (b) a variant of the cavity method, used widely in prior rigorous and heuristic treatments of classical spin glasses. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02768 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The free energy limit of the SYK model at high temperature Gamarnik, David Pernice, Francisco Schmidhuber, Alexander Zlokapa, Alexander Disordered Systems and Neural Networks High Energy Physics - Theory Probability Quantum Physics The Sachdev-Ye-Kitaev (SYK) model is a disordered quantum mean-field model studied in condensed matter physics and the holographic theory of black holes. Its structural properties can be derived heuristically using a combination of the replica method and path integration techniques. Analyzing it mathematically rigorously, however, turned out to be notoriously difficult, even for basic questions such as computing the annealed free energy. In this paper we rigorously compute the free energy limit (annealed and quenched) for this model at high enough but constant temperature. Our results are in numerical agreement with the results derived by physics methods. Remarkably, though, our method of proof is novel and is different from the physics approach. It is based on (a) the theory of the component structure of sparse random graphs and (b) a variant of the cavity method, used widely in prior rigorous and heuristic treatments of classical spin glasses. |
| title | The free energy limit of the SYK model at high temperature |
| topic | Disordered Systems and Neural Networks High Energy Physics - Theory Probability Quantum Physics |
| url | https://arxiv.org/abs/2605.02768 |