Graphical Representations of Lattice Spin Models

The material presented in this book corresponds to the content of a series of four lectures given by the author at Collège de France in January 2015, as well as a class given in Princeton from March to May 2015. The aim is to provide an introduction to the theory of graphical representations and its applications to so-called spin models.

We chose to present a few examples of recent results proved using graphical representations. Since the range of applications is very wide, we selected results dealing with classical spin models such as the Ising and Potts models.

The text requires very little background from probability or mathematical physics. While mainly intended for researchers, the manuscript has been written as lecture notes accessible to young motivated PhD students in probability and mathematical physics.