UBC DG-MP-PDE Seminar: Daniel Hadas

  • Date: 11/03/2021
  • Time: 15:30
Lecturer(s):
Daniel Hadas, Tel Aviv University
Location: 

Online

Topic: 

Random High-density Packings of 2x2 Tiles on the Square Lattice

Description: 

Abstract:
Random high-density packings of 2x2 tiles on the square lattice Abstract: Consider random configurations of disjoint 2x2 tiles positioned in integer coordinates in a bounded domain in R², where the probability for the appearance of a configuration is proportional to λⁿ, with n being the number of tiles in the configuration. This is called the 2x2-Hard-Squares model with fugacity λ. Many similar hard-core lattice gases undergo a phase transition: at low-fugacities the random configuration is disordered with exponential decay of correlations while at high fugacities the random configuration globally approximates a single optimally-packed configuration. This paradigm is inapplicable to the 2x2-hard-squares model due to a “sliding” degree of freedom in the optimal packing, and the question of its high-fugacity behavior remained open. We show that at high fugacities, the 2x2 hard-squares model exhibits a columnar phase: the tiles either preferentially occupy the even rows, the odd rows, the even columns or the odd columns.

Other Information: 

Zoom Talk

For the zoom link, contact spicard@math.ubc.ca

 

Event website:
https://www.math.ubc.ca/events/oct-6-2021-random-high-density-packings-2x2-tiles-square-lattice