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Two dimensional Ising model with columnar disorder and continuum limit of random matrix products

Presented by: 
Gianbattista Giacomin
Friday 14th December 2018 - 14:30 to 15:30
INI Seminar Room 1
I will present results taken from a recent work with R. L. Greenblatt and F. Comets on the continuum limit of random matrix products. The focus will be on one of the applications: two dimensional Ising model with columnar disorder. 50 years ago McCoy and Wu pointed out that the free energy density of the two dimensional Ising model (on the square lattice, with nearest neighbor interactions) can be written in terms of the Lyapunov exponent of products of suitable random two by two matrices. Moreover they extracted from this remarkable formula a number of (even more remarkable) conclusions. I will present their approach and explain how some of the steps can be made mathematically rigorous. I will also explain what is missing to get to the McCoy and Wu conclusions.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons