Affine dimers from characteristic polygons

  • Daniel Holmes University of Cambridge, DPMMS
Keywords: dimer model; hyperplane arrangement; torus; lattice polygon


Recent work by Forsgård indicates that not every convex lattice polygon arises as the characteristic polygon of an affine dimer or, equivalently, an admissible oriented line arrangement on the torus in general position. We begin the classication of convex lattice polygons arising as characteristic polygons of affine dimers. We present several general constructions of new affine dimers from old, and an algorithm for finding affine dimers with prescribed polygon.

With these tools we prove that all lattice triangles, generalised parallelograms, and polygons of genus at most two admit an affine dimer.

How to Cite
Holmes, D. (2022). Affine dimers from characteristic polygons. The PUMP Journal of Undergraduate Research, 5, 24-51.