Random Walks, Critical Phenomena, and Triviality in Quantum Field Theory

The subject of this book is equilibrium statistical mechanics, in particular the theory of critical phenomena, and quantum field theory. It addresses both researchers and students in mathematics and physics.

Inhalt

1. General introduction.- 2. Phase transitions and critical points in classical spin systems: A brief survey.- 3. Scale transformations and scaling (continuum) limits in lattice spin systems.- 4. Construction of scaling limits: the renormalization group.- 5. Random walks as Euclidean field theory (EFT).- 6. EFT as a gas of random walks with hard-core interactions.- 7 Random-surface models.- 8. Introduction.- 9 Random-walk models in the absence of magnetic field.- 10. Random-walk models in the presence of a magnetic field.- 11. Factorization and differentiation of the weights.- 12. Correlation inequalities: A survey of results.- 13. Background material.- 14. Inequalities for critical exponents.- 15. Continuum Limits.- References.