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SUMMARY:Mini-Cours:  Disordered Ising chains and products of random transf
 er matrices.
DTSTART:20231208T093000Z
DTEND:20231208T113000Z
DTSTAMP:20260523T013700Z
UID:indico-event-10156@indico.math.cnrs.fr
CONTACT:guillaume.barraquand@math.cnrs.fr
DESCRIPTION:Speakers: Giambattista Giacomin\n\nAbstract: it is well known 
 (and rather elementary\, as we will explain) that the partition function o
 f the Ising chain can be expressed in terms of products of 2 by 2 matrices
 . In particular the free energy density of the model is just the leading e
 igenvalue of the transfer matrix if the model is homogeneous. In presence 
 of disorder\, the transfer matrix structure is still available\, but one d
 eals with products of random (still 2 by 2) matrices and\, in particular\,
  the free energy density is\, in this inhomogeneous setting\, the leading 
 Lyapunov exponent of the matrix product. The aim of the lecture is to intr
 oduce the transfer matrix formalism and analyze both the singular behavior
  of the free energy density in the strong interaction limit and the behavi
 or of the configurations of the system in this limit. The presentation wil
 l be mostly restricted to the case in which the external field is centered
 : this is both for time reasons and because the understanding of the cente
 red case is much more advanced. The final aim is to show that the results 
 that we will present (hopefully\, with some ideas from the proofs) confirm
  predictions made in the physics literature by applying a renormalization 
 group procedure introduced by D. Fisher in the 90s.\n\nhttps://indico.math
 .cnrs.fr/event/10156/
LOCATION:Salle Mirzakhani (201)
URL:https://indico.math.cnrs.fr/event/10156/
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