Alexi Morin Duchesne

In this course, we will study families of models in statistical mechanics in one and two dimensions that are defined on a lattice and have large numbers of degrees of freedom. We will focus on models that are endowed with certain large symmetry groups, and are thus called “integrable models”. Such models include the Q-state Potts model, the dimer model, the model of bond percolation, the XXZ spin chain, and the dense loop models. We will investigate advanced techniques in mathematical physics that allow us to compute the eigenvalues of their Hamiltonians, and in some cases their partition functions.