Cari,
vi scrivo per annunciare il seminario di Leonardo Lelli il 2 febbraio 2024 alle ore 14 in Sala di Consiglio presso il Dipartimento di Matematica Guido Castelnuovo, Sapinza Università di Roma, Piazzale Aldo Moro, 5 Roma
............................................................................................................. Title Zero-temperature stochastic Ising model on quasi-transitive graphs
Abstract
We examine the question of fixation for zero-temperature stochastic Ising model on some connected quasi-transitive graphs. The initial spin configuration is distributed according to a Bernoulli product measure with parameter $p\in (0,1) $.
We prove that the shrink property for the underlying graph is a necessary condition for all sites to flip infinitely often almost surely (in this case the model is said of type I).
Our main result shows that if $p=1/2 $ and the graph is connected and invariant under rotations and translations, then a strengthening of the shrink property, called the planar shrink property, implies that the model is of type I. We provide an infinite class of graphs having the planar shrink property. Finally, we prove that for one-dimensional translation invariant graphs, the shrink property is a necessary and sufficient condition for the model to be of type I. This talk is based on joint work with my thesis advisor Emilio De Santis.
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Cordiali saluti, Emilio De Santis