Department of Mathematics - Mathematics Colloquium - Two dimensional dimers beyond planarity

We study the dimer model and the monomer double dimer model, and prove that on two-dimension like graphs (not necessarily planar), both the correlation function and the loop connectivity probability decays to zero. Our analysis is by introducing a new (complex) spin representation for all models belonging to this class, and by deriving a new proof of the Mermin-Wagner theorem which does not require the positivity of the Gibbs measure. Based on joint work with Lorenzo Taggi (Sapienza Univ. di Roma).