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02 09 im noticia Dyson models with random boundary conditionsTítulo: Dyson models with random boundary conditions

Palestrante: Aernout van Enter (Groningen University)
Data: 06/09/2021
Horário: 15:00h
Local: Transmissão online.

Confira AQUI o link para transmissão.

Resumo: I discuss the low-temperature behaviour of Dyson models (polynomially decaying long-range Ising models in one dimension) in the presence of random boundary conditions. As for typical random (i.i.d.) boundary conditions Chaotic Size Dependence occurs, that is, the pointwise thermodynamic limit of the finite-volume Gibbs states for increasing volumes does not exist, but the sequence of states moves between various possible limit points, as a consequence it makes sense to study distributional limits, the so-called "metastates" which are measures on the possible limiting Gibbs measures.

The Dyson model is known to have a phase transition for decay parameters α between 1 and 2. We show that the metastate changes character at α =3/2. It is dispersed in both cases, but it changes between being supported on two pure Gibbs measures when α is less than 3/2 to being supported on mixtures thereof when α is larger than 3/2.

Joint work with Eric Endo and Arnaud Le Ny

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