Chaos in the thermal regime for pinned manifolds via functional RG
| dc.creator | Duemmer, O. | |
| dc.creator | Doussal, P. Le | |
| dc.date | 2007-09-10 | |
| dc.date.accessioned | 2026-07-07T08:28:30Z | |
| dc.date.available | 2026-07-07T08:28:30Z | |
| dc.description | The statistical correlations of two copies of a d-dimensional elastic manifold embedded in slightly different frozen disorder are studied using the Functional Renormalization Group to one-loop accuracy, order O(eps = 4-d). Determining the initial (short scale) growth of mutual correlations, i.e. chaos exponents, requires control of a system of coupled differential (FRG) equations (for the renormalized mutual and self disorder correlators) in a very delicate boundary layer regime. Some progress is achieved at non-zero temperature, where linear analysis can be used. A growth exponent a is defined from center of mass fluctuations in a quadratic potential. In the case where temperature is marginal, e.g. a periodic manifold in d=2, we demonstrate analytically and numerically that a = eps (1/3 - 1/(2 log(1/T)) with interesting and unexpected logarithmic corrections at low T. For short range (random bond) disorder our analysis indicates that a = 0.083346(6) eps, with large finite size corrections. | |
| dc.description | 14 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/0709.1378 | |
| dc.identifier | http://arxiv.org/abs/0709.1378 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/137642 | |
| dc.subject | Disordered Systems and Neural Networks | |
| dc.title | Chaos in the thermal regime for pinned manifolds via functional RG | |
| dc.type | text |