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An exposition to information percolation for the Ising model
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Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 24 (2015) no. 4, pp. 745-761.

Information percolation is a new method for analyzing stochastic spin systems through classifying and controlling the clusters of information-flow in the space-time slab. It yielded sharp mixing estimates (cutoff with an O(1)-window) for the Ising model on d up to the critical temperature, as well as results on the effect of initial conditions on mixing. In this expository note we demonstrate the method on lattices (more generally, on any locally-finite transitive graph) at very high temperatures.

La percolation de l’information est une nouvelle méthode pour analyser les systèmes de spins stochastiques à travers la classification et le contrôle des amas de flots d’information dans des tranches d’espace-temps. Elle fournit des estimées fines de mélange (transition abrupte dans une fenêtre d’ordre O(1)) pour le modèle d’Ising sur d jusqu’à la température critique, ainsi que des résultats sur l’influence des conditions initiales sur le mélange. Dans cet article de présentation, nous appliquons cette méthode à des réseaux (plus généralement, sur tout graphe localement fini et transitif) à très haute température.

Published online : 2016-01-21
@article{AFST_2015_6_24_4_745_0,
     author = {Eyal Lubetzky and Allan Sly},
     title = {An exposition to information percolation for the Ising model},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 24},
     number = {4},
     year = {2015},
     pages = {745-761},
     zbl = {1333.60207},
     language = {en},
     url={afst.centre-mersenne.org/item/AFST_2015_6_24_4_745_0/}
}
Lubetzky, Eyal; Sly, Allan. An exposition to information percolation for the Ising model. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 24 (2015) no. 4, pp. 745-761. https://afst.centre-mersenne.org/item/AFST_2015_6_24_4_745_0/

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