Non-equilibrium dynamics of polymers and interfaces in random media : conjecture $ψ=d_s/2$ for the barrier exponent
| dc.creator | Monthus, Cecile | |
| dc.creator | Garel, Thomas | |
| dc.date | 2007-12-20 | |
| dc.date.accessioned | 2026-07-07T09:24:29Z | |
| dc.date.available | 2026-07-07T09:24:29Z | |
| dc.description | We consider various random models (directed polymer, random ferromagnets, spin-glasses) in their disorder-dominated phases, where the free-energy cost $F(L)$ of an excitation of length $L$ presents fluctuations that grow as a power-law $ΔF(L) \sim L^θ$ with the 'droplet' exponent $θ$. Within the droplet theory, the energy and entropy of such excitations present fluctuations that grow as $ΔE(L) \sim ΔS(L) \sim L^{d_s/2}$ where $d_s$ is the dimension of the surface of the excitation. These systems usually present a positive 'chaos' exponent $ζ=d_s/2-θ>0$, meaning that the free-energy fluctuation of order $L^θ$ is a near-cancellation of much bigger energy and entropy fluctuations of order $L^{d_s/2}$. Within the standard droplet theory, the dynamics is characterized by a barrier exponent $ψ$ satisfying the bounds $θ\leq ψ\leq d-1$. In this paper, we argue that a natural value for this barrier exponent is $ψ=d_s/2$ : (i) for the directed polymer where $d_s=1$, this corresponds to $ψ=1/2$ in all dimensions; (ii) for disordered ferromagnets where $d_s=d-1$, this corresponds to $ψ=(d-1)/2$; (iii) for spin-glasses where interfaces have a non-trivial dimension $d_s$ known numerically, our conjecture $ψ=d_s/2$ gives numerical predictions in $d=2$ and $d=3$. We compare these values with the available numerical results for each case, in particular with the measure $ψ\simeq 0.49$ of Kolton, Rosso, Giamarchi, Phys. Rev. Lett. 95, 180604 (2005) for the non-equilibrium dynamics of a directed elastic string. | |
| dc.description | 8 pages, comments welcome | |
| dc.identifier | https://arxiv.org/abs/0712.3358 | |
| dc.identifier | http://arxiv.org/abs/0712.3358 | |
| dc.identifier | J. Phys. A: Math. Theor., 41 (2008) 115002 | |
| dc.identifier | doi:10.1088/1751-8113/41/11/115002 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/156113 | |
| dc.subject | Disordered Systems and Neural Networks | |
| dc.title | Non-equilibrium dynamics of polymers and interfaces in random media : conjecture $ψ=d_s/2$ for the barrier exponent | |
| dc.type | text |