Seminar Interacting Random Systems

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Mittwoch, 20.01.2021, 11:30 Uhr (Online Event)
Lorenzo Taggi, University of Rome “La Sapienza”, Italien:
Exponential decay of correlations for O(N) spin systems
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Online Event

Abstrakt
The Spin O(N) model is a classical statistical mechanics model whose configurations are collections of unit vectors, called spins, taking values on the surface of a N ?1 dimensional unit sphere, with each spin associated to the vertex of a graph. Some special cases of the spin O(N) model are the Ising model (N = 1), the XY model (N = 2), and the classical Heisenberg model (N = 3). Despite the fact that it is a very classical model, there remain important gaps in understanding, particularly in the case N > 2. This talk will provide an introduction on this class of models and present a new recent result about exponential decay of correlations for arbitrary (non-zero) values of the external magnetic field and arbitrary spin dimension N>1. The proof of this result employs a representation of the model as a system of coloured random paths and a sampling procedure, which allows us to bound from above the "typical lenght" of the open paths. The talk is based on a joint work with B. Lees.

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Seminar Interacting Random Systems

Veranstalter
WIAS Berlin
Mittwoch, 03.02.2021, 11:30 Uhr (Online Event)
Elena Pulvirenti, Delft University of Technology, Niederlande:
The Widom-Rowlinson model: metastability, mesoscopic and microscopic fluctuations for the critical droplet (online talk)
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Online Event

Abstrakt
We introduce the equilibrium Widom-Rowlinson model on a two-dimensional finite torus in which the energy of a particle configuration is attractive and determined by the union of small discs centered at the positions of the particles. We then discuss the metastable behaviour of a dynamic version of the WR model. This means that the particle configuration is viewed as a continuous time Markov process where particles are randomly created and annihilated as if the outside of the torus were an infinite reservoir with a given chemical potential. In particular, we start with the empty torus and are interested in the first time when the torus is fully covered by discs in the regime at low temperature and when the chemical potential is supercritical. In order to achieve the transition from empty to full, the system needs to create a sufficiently large droplet, called critical droplet, which triggers the crossover. We compute the distribution of the crossover time and identify the size and the shape of the critical droplet. The analysis relies on a mesoscopic and microscopic description of the surface of the critical droplet. It turns out that the critical droplet is close to a disc of a certain deterministic radius, with a boundary that is random and consists of a large number of small discs that stick out by a small distance. We will show how the analysis of surface fluctuations in the WR model allows us to derive the leading order term of the condensation time and also the correction order term. This is a joint work with Frank den Hollander (Leiden), Sabine Jansen (Munich) and Roman Kotecky (Prague & Warwick).

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Seminar Interacting Random Systems

Veranstalter
WIAS Berlin
Due to the COVID 19 pandemic, events are currently taking place under restricted circumstances. We offer the seminar online, besides the opportunity to attend it in person in rooms 405/406. As these rooms have a limited capacity of 12 persons, due to hygiene recommendations, we kindly ask those who want to participate in person to register (put your name in the list) in the following google document. If 12 have already registered, please follow the streamed talk. The organisers will send the zoom link shortly before the time of the talk. Please contact the organisers if you are not included in the email list and you want to follow the talk or be kept up to date with the seminar.

Zoom link

Organisers: Luisa Andreis and Willem van Zuijlen