Benvenuti nell'Anagrafe della Ricerca d'Ateneo
La valutazione delle attività di ricerca che si svolgono nelle università ha assunto un'importanza rilevante sia per l'intero sistema universitario sia all'interno di ogni singolo ateneo. Roma Tre si è quindi dotata di idonei strumenti informativi in grado di supportare al meglio le azioni di monitoraggio e di valutazione delle attività di ricerca svolte nei propri dipartimentied ha realizzato una Anagrafe della Ricerca di Ateneo.
EnglishWe consider the Glauber dynamics for the 2D Ising model in a box of side L, at inverse temperature β and random boundary conditions τ whose distribution P either stochastically dominates the extremal plus phase (hence the quotation marks in the title) or is stochastically dominated by the extremal minus phase. A particular case is when P is concentrated on the homogeneous configuration identically equal to + (equal to −). For β large enough we show that for any ε > 0 there exists c = c(β, ε) such that the corresponding mixing time Tmix satisfies limL→∞ P (Tmix ≥ exp(cLε)) = 0. In the non-random case τ ≡ + (or τ ≡ −), this implies that Tmix ≤ exp(cLε). The same bound holds when the boundary conditions are all + on three sides and all − on the remaining one. The result, although still very far from the expected Lifshitz behavior Tmix = O(L2), considerably improves upon the previous known estimates of the form Tmix ≤ exp(cL 12 +ε). The techniques are based on induction over length scales, combined with a judicious use of the so-called “censoring inequality” of Y. Peres and P. Winkler, which in a sense allows us to guide the dynamics to its equilibrium measure.
Martinelli F, & Toninelli FL (2010). On the Mixing Time of the 2D Stochastic Ising Model with "Plus" Boundary Conditions at Low Temperature. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 296(1), 175-213 [10.1007/s00220-009-0963-5].
| Titolo: | On the Mixing Time of the 2D Stochastic Ising Model with "Plus" Boundary Conditions at Low Temperature | |
| Autori: | ||
| Data di pubblicazione: | 2010 | |
| Rivista: | ||
| Citazione: | Martinelli F, & Toninelli FL (2010). On the Mixing Time of the 2D Stochastic Ising Model with "Plus" Boundary Conditions at Low Temperature. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 296(1), 175-213 [10.1007/s00220-009-0963-5]. | |
| Abstract: | We consider the Glauber dynamics for the 2D Ising model in a box of side L, at inverse temperature β and random boundary conditions τ whose distribution P either stochastically dominates the extremal plus phase (hence the quotation marks in the title) or is stochastically dominated by the extremal minus phase. A particular case is when P is concentrated on the homogeneous configuration identically equal to + (equal to −). For β large enough we show that for any ε > 0 there exists c = c(β, ε) such that the corresponding mixing time Tmix satisfies limL→∞ P (Tmix ≥ exp(cLε)) = 0. In the non-random case τ ≡ + (or τ ≡ −), this implies that Tmix ≤ exp(cLε). The same bound holds when the boundary conditions are all + on three sides and all − on the remaining one. The result, although still very far from the expected Lifshitz behavior Tmix = O(L2), considerably improves upon the previous known estimates of the form Tmix ≤ exp(cL 12 +ε). The techniques are based on induction over length scales, combined with a judicious use of the so-called “censoring inequality” of Y. Peres and P. Winkler, which in a sense allows us to guide the dynamics to its equilibrium measure. | |
| Handle: | http://hdl.handle.net/11590/138037 | |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
File in questo prodotto:
http://hdl.handle.net/11590/138037
Copyright © 2021