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Full Description
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.
The book begins with critical behaviour and its basic discussion in statistical mechanics models, and subsequently explores perturbative and non-perturbative analysis in the renormalisation group. Lastly it discusses the relation of these topics to the self-avoiding walk and supersymmetry.
Including exercises in each chapter to help readers deepen their understanding, it is a valuable resource for mathematicians and mathematical physicists wanting to learn renormalisation group theory.
Contents
- Part I Spin Systems and Critical Phenomena. - Spin Systems. - Gaussian Fields. - Finite-Range Decomposition. - The Hierarchical Model. - Part II The Renormalisation Group: Perturbative Analysis. - The Renormalisation Group Map. - Flow Equations and Main Result. - Part III The Renormalisation Group: Nonperturbative Analysis. - The Tz-Seminorm. - Global Flow: Proof of Theorem 4.2.1. - Nonperturbative Contribution to ΦU/+: Proof of Theorem 8.2.5. - Bounds on ΦK/+ : Proof of Theorem 8.2.4. - Part IV Self-AvoidingWalk and Supersymmetry. - Self-AvoidingWalk and Supersymmetry. - Part V Appendices. - Appendix A: Extension to Euclidean Models. - Appendix B: Solutions to Exercises.
