Izabella STUHL - Hard-core models in 2D lattices
schedule le mardi 26 novembre 2019 de 14h00 à 15h00
Organisé par : LPSM
Intervenant : Izabella STUHL (Penn State Univ.)
Lieu : Jussieu, tours 16-26, 2ème étage, salle 209.
Sujet : Izabella STUHL - Hard-core models in 2D lattices
One of the outstanding open problems of statistical mechanics is whether non-overlapping hard disks of the same diameter in the plane admit a unique Gibbs measure at high density, i.e., whether this system exhibits or not a phase transition.
It is natural to approach this question by using a discrete version of the model where the disk centers must be at sites of a lattice, say a unit triangular lattice A2 or a unit square lattice Z2, and let the Euclidean diameter D of the hard disks tend to innity.
We provide a complete solution of this problem, for both A2 and Z2, with the help of the Pirogov-Sinai theory (in the case of Z2 in absence of sliding). In both cases the crucial aspect is number-theoretic properties of the diameter D. Answers are provided in terms of Eisenstein primes for A2 and norm equations in the cyclotomic integer ring Z[ζ] for Z2, where ζ is a primitive 12th root of unity.
This is a joint work with A. Mazel and Y. Suhov.