# Seminars & Colloquia Calendar

Mathematical Physics Seminar

## The high-density phase transition for the high-density hard-core model on a triangular lattice

#### Yuri Suhov - University of Cambridge

Location:  Hill 705
Date & time: Thursday, 26 April 2018 at 2:00PM - 3:00PM

Abstract:  The high-density hard-core configuration model has attracted attention for quite a long time; first rigorous results about the phase transition on a lattice where published by Dobrushin in late 1960s. Since then, various aspects of the model became important in a number of applications. We propose a solution for the model on a triangular lattice. The phase diagram (i.e., the collection of shift-periodic pure phases) depends on arithmetic properties of the exclusion distance $$D$$; a convenient classification of possible cases can be given in terms of Eisenstein primes.

For two classes of values of $$D$$ the phase diagrams is completely specified:

(I) when either $$D$$ or $$D/{\sqrt 3}$$ is a positive integer whose prime decomposition does not contain factors of the form $$6k+1$$,

(II) when $$D^2$$ is an integer whose prime decomposition contains (i) a single prime of the form $$6k+1$$, and (ii) other primes, if any, in even powers, except for the prime $$3$$. For the remaining values of $$D$$ we offer some partial results supported by computer simulations. The main method of proof is the Pirogov-Sinai theory complemented by Zahradnik's argument and the Dominated ground state theory.

This is a joint work with A. Mazel and Y. Suhov.

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