Bauerschmidt R., Brydges D.C., Slade G. Introduction to a Renormalisation Group Method

Springer, 2019. — 283 p. — (Lecture Notes in Mathematics 2242). — ISBN: 9813295910.This is a primer on a mathematically rigorous renormalisation group theory, presenting mathematical techniques fundamental to renormalisation group analysis such as Gaussian integration, perturbative renormalisation and the stable manifold theorem. It also provides an overview of fundamental models in statistical mechanics with critical behaviour, including the Ising and φ4 models and the self-avoiding walk.Spin Systems
Gaussian Fields
Finite-Range Decomposition
The Hierarchical Model
The Renormalisation Group Map
Flow Equations and Main Result
The T z-Seminorm
Global Flow: Proof of Theorem 4.2.1
Nonperturbative Contribution to Φ U+ : Proof of Theorem 8.2.5
Bounds on ΦK+ : Proof of Theorem 8.2.4
Self-Avoiding Walk and Supersymmetry
Appendix A: Extension to Euclidean Models
Appendix B: Solutions to Exercises