Tom Kennedy: The Newton method for fixed points of renormalization group maps for statistical mechanical systems

The renormalization group (RG) relates the critical behavior of a statistical mechanical model to the behavior of the RG map in a neighborhood of a fixed point. This map has a finite number of expanding directions at the fixed point which are related to critical exponents of the model. One would like to use the Newton method to find the fixed point. However, many RG maps have an eigenvalue of +1 in the linearization which prevents this. We show how a simple trick can change this +1 eigenvalue to -1, making the application of the Newton method possible. To make this talk accessible , I will start with a review of the RG in both the Wilson-Kadanoff real-space formulation and the tensor network approach. This is joint work with Nikolay Ebel and Slava Rychkov.