Title: Gibbs measures for 3x1 Domino tilings

Abstract:

For the classic case of 2x1 dominos the set of Gibbs measures on tilings is completely understood and depends on 2 parameters known as the horizontal and vertical slope of the measure. Using a generalization of the well known height function, we will show why such a result cannot be expected when we switch to 3x1 dominos and why the dimension of this space is exploding. We will give a detailed suggestion of what could be a description of this space.