A simple one dimensional glassy Kac model
| dc.creator | Montanari, Andrea | |
| dc.creator | Sinton, Antoine | |
| dc.date | 2007-05-01 | |
| dc.date.accessioned | 2026-07-07T13:02:14Z | |
| dc.date.available | 2026-07-07T13:02:14Z | |
| dc.description | We define a new family of random spin models with one-dimensional structure, finite-range multi-spin interactions, and bounded average degree (number of interactions in which each spin participates). Unfrustrated ground states can be described as solutions of a sparse, band diagonal linear system, thus allowing for efficient numerical analysis. In the limit of infinite interaction range, we recover the so-called XORSAT (diluted p-spin) model, that is known to undergo a random first order phase transition as the average degree is increased. Here we investigate the most important consequences of a large but finite interaction range: (i) Fluctuation-induced corrections to thermodynamic quantities; (ii) The need of an inhomogeneous (position dependent) order parameter; (iii) The emergence of a finite mosaic length scale. In particular, we study the correlation length divergence at the (mean-field) glass transition. | |
| dc.description | 25 pages, 9 eps figures | |
| dc.identifier | https://arxiv.org/abs/0705.0054 | |
| dc.identifier | http://arxiv.org/abs/0705.0054 | |
| dc.identifier | J. Stat. Mech. (2007) P08004 | |
| dc.identifier | doi:10.1088/1742-5468/2007/08/P08004 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/226382 | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Disordered Systems and Neural Networks | |
| dc.title | A simple one dimensional glassy Kac model | |
| dc.type | text |