Speaker
Hjalmar Rosengren, Chalmers University of Technology and University of Gothenburg
Abstract
There are many useful links between solvable lattice models and discrete geometry. One such link that seems to be missing from the literature is that the free-fermionic case of Baxter’s elliptic SOS model corresponds to two-periodic biased domino tilings. That is, dominos tiling of a square lattice are weighted independently depending both on their orientation and their position (relative to a checkerboard pattern). Using this connection, and the tangent method of Colomo-Sportiello, we compute the corresponding arctic curve on the Aztec diamond. It turns out to be algebraic of order 8. Our method contains non-rigorous steps, but the result agrees with known special cases and with numerical experiments.
This work is joint with N. Robert, P. Ruelle and C. Walmsley Hagendorf (all at Université Catholique de Louvain).