The Infrared Bound Without Reflection Positivity

To shake things up a little we’ll talk about the Ising model. I will explain a phenomenon in thermodynamics called the “infrared bound”, and what it is usually good for. The only known way to prove this bound on a graph is using a property called “reflection positivity”. But this basically limits the graph in question to Z^d, the Euclidean lattice.

Recently with Tom Meyerovitch we have been thinking of a new method of proving the infrared bound on other (transitive) graphs. I will present a necessary and sufficient condition for something called “Gaussian domination” which in turn implies the infrared bound. The main idea of the talk is to present the different ideas that arise in these kinds of thermodynamic models.

No background is assumed.