Academic Journal
Fluctuations of the Free Energy of the Spherical Sherrington–Kirkpatrick Model with Heavy-Tailed Interaction: Fluctuations of the free energy of the spherical Sherrington-Kirkpatrick model with heavy-tailed interaction
| Title: | Fluctuations of the Free Energy of the Spherical Sherrington–Kirkpatrick Model with Heavy-Tailed Interaction: Fluctuations of the free energy of the spherical Sherrington-Kirkpatrick model with heavy-tailed interaction |
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| Authors: | Kim, Taegyun, Lee, Ji Oon |
| Source: | Journal of Statistical Physics. 191 |
| Publication Status: | Preprint |
| Publisher Information: | Springer Science and Business Media LLC, 2024. |
| Publication Year: | 2024 |
| Subject Terms: | Equilibrium statistical mechanics, heavy-tailed matrix, phase transition, Probability (math.PR), FOS: Mathematics, FOS: Physical sciences, Applications of statistical mechanics to specific types of physical systems, Mathematical Physics (math-ph), Probability theory on algebraic and topological structures, SSK model, free energy, Mathematics - Probability, Mathematical Physics |
| Description: | We consider the 2-spin spherical Sherrington--Kirkpatrick model without external magnetic field where the interactions between the spins are given as random variables with heavy-tailed distribution. We show that the free energy exhibits a sharp phase transition depending on the location of the largest eigenvalue of the interaction matrix. We also prove the order of the limiting free energy and the limiting distribution of the fluctuation of the free energy for both regimes. 32 pages |
| Document Type: | Article |
| File Description: | application/xml |
| Language: | English |
| ISSN: | 1572-9613 |
| DOI: | 10.1007/s10955-024-03358-w |
| DOI: | 10.48550/arxiv.2402.14295 |
| Access URL: | http://arxiv.org/abs/2402.14295 |
| Rights: | Springer Nature TDM arXiv Non-Exclusive Distribution |
| Accession Number: | edsair.doi.dedup.....65aae25a94dac3e36a52373b64fcd1a5 |
| Database: | OpenAIRE |
| ISSN: | 15729613 |
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| DOI: | 10.1007/s10955-024-03358-w |