[Seminario] INVITACION SEMINARIO CONJUNTO DE MODELAMIENTO ESTOCÁSTICO Y NÚCLEO MILENIO MESCD, LUNES 25 DE JULIO ALAS 16:30 HRS.

[Maria Ines]

Estimados Académicos y Alumnos,

Se les invita para el próximo Lunes 25 de Julio a las  16:30 hrs, al 
Seminario CONJUNTO DE MODELAMIENTO ESTOCÁSTICO Y NÚCLEO MILENIO MESCD, 
este seminario se realizará en la Sala de Seminarios John Von Neumann 
CMM, Torre Norte piso 7 de Beauchef 851.

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SEMINARIO

CONJUNTO DE MODELAMIENTO ESTOCÁSTICO Y NÚCLEO MILENIO MESCD.

EXPOSITOR

Jorge Littin

TÍTULO

Phase Transitions on the Long Range Ising Models in presence of an 
random external field

Resumen:*/

We study the ferromagnetic one-dimensiosnal Random Field Ising Model 
with (RFIM) in presence of an external random field. The interaction 
between two spins decays as $d^{\alpha-2}$ where $d$ is the distance 
between two sites and $\alpha \in [0,1/2)$ is a parameter of the model. 
We consider an external random field on $\mathbb{Z}$ with independent 
but not identically distributed random variables. Specifically for each 
$i \in \mathbb{Z}$, the distribution of $h_i$ is
$P[h_i=\pm \theta(1+|i|)^{-\nu/2}]$.

This work, whose main goal is the study of the existence of a phase 
transition at a strictly positive temperature for different values of 
$\nu$ is inspired on the very recent article [2] where the 2D Ising 
Model with spatially dependent but not random external field is studied. 
In the random case, we combine some of the martingale difference 
techniques used in the previous articles of Cassandro, Picco and Orlandi 
[3], and the Aizemann & Wehr method [3]. Some of the classical results, 
the key parts of this work and some of the technical difficulties will 
be discussed in this talk.

Joint work with Pierre Picco

References:

[1] M. Aizenman and C. M. Newman. Discontinuity of the percolation 
density in one-dimensional 1/|x - y|, 107(4):611--647, 1986.

[2] Rodrigo Bissacot, Marzio Cassandro, Leandro Cioletti, and Errico 
Presutti. Phase transitions in ferromagnetic ising models with spatially 
dependent magnetic fields. Communications in Mathematical Physics, 
337(1):41--53, 2015.

[3] Marzio Cassandro, Enza Orlandi, and Pierre Picco. Phase transition 
in the 1d random field Ising model with long range interaction. 
Communications in Mathematical Physics, 288(2):731--744, 2009.

Fecha: Lunes 25 de Julio, 16:30 hrs.
Lugar: Centro de Modelamiento matemático, Universidad de Chile (Sala de 
Seminarios, 7° piso).

Esperando contar con su presencia, les saluda,

Ma. Inés Rivera

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