Some New Results on the Kinetic Ising Model in a Pure Phase
| dc.creator | Bodineau, T. | |
| dc.creator | Martinelli, F. | |
| dc.date | 2002-02-08 | |
| dc.date.accessioned | 2026-07-07T04:28:58Z | |
| dc.date.available | 2026-07-07T04:28:58Z | |
| dc.description | We consider a general class of Glauber dynamics reversible with respect to the standard Ising model in $\bbZ^d$ with zero external field and inverse temperature $\gb$ strictly larger than the critical value $\gb_c$ in dimension 2 or the so called ``slab threshold'' $\hat \b_c$ in dimension $d \geq 3$. We first prove that the inverse spectral gap in a large cube of side $N$ with plus boundary conditions is, apart from logarithmic corrections, larger than $N$ in $d=2$ while the logarithmic Sobolev constant is instead larger than $N^2$ in any dimension. Such a result substantially improves over all the previous existing bounds and agrees with a similar computations obtained in the framework of a one dimensional toy model based on mean curvature motion. The proof, based on a suggestion made by H.T. Yau some years ago, explicitly constructs a subtle test function which forces a large droplet of the minus phase inside the plus phase. The relevant bounds for general $d\ge 2$ are then obtained via a careful use of the recent $\bbL^1$--approach to the Wulff construction. Finally we prove that in $d=2$ the probability that two independent initial configurations, distributed according to the infinite volume plus phase and evolving under any coupling, agree at the origin at time $t$ is bounded from below by a stretched exponential $\exp(-\sqrt{t})$, again apart from logarithmic corrections. Such a result should be considered as a first step toward a rigorous proof that, as conjectured by Fisher and Huse some years ago, the equilibrium time auto-correlation of the spin at the origin decays as a stretched exponential in $d=2$. | |
| dc.identifier | https://arxiv.org/abs/math-ph/0202013 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0202013 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/56992 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Probability | |
| dc.subject | 82B10, 82B20, 60K35 | |
| dc.title | Some New Results on the Kinetic Ising Model in a Pure Phase | |
| dc.type | text |