12/11/2025, 16:00 — 17:00 — Online
Orphée Collin, TU Wien
The random field Ising chain in the large interaction limit
We are going to present recent results and ongoing research concerning the Ising chain (i.e., the Ising model in dimension 1) with homogeneous (large) spin-spin interaction, but subjected to a random external field, the latter being sampled from an i.i.d sequence. The framework is that of disordered systems. We will first present the pure model (homogeneous external field) which is exactly solvable. Then we will turn to the disordered model, showing that for this model the disorder is strongly relevant, through estimates on the free energy and a description of the typical configurations. There are two distinct cases with qualitatively different behaviours: the cases of centered or uncentered disorder. We will also present a continous analogue of the model, obtained by a weak disorder limit, which has the advantage of allowing some explicit computations. Our approach confirms and deepens claims made in the physics literature by D. Fisher and collaborators, based on a study of the Glauber dynamics of the model using the renormalisation group method.
