Master Class "Advanced Statistical Field Theory"

Class on the Relation of the Manna Model to Depinning, 4/2019

About the Course

This course will provide you with a deeper understanding of field theory, universality and the renormalization group. Applications range from the large-scale structure in the universe over magnets to your coffee cup. Basic knowledge of field theory is required. We start with a review of the basics, including φ⁴-theory, Gaussian integrals, and the path integral. While most applications are chosen for simplicity from statistical mechanics, the methods are general, and useful in high-energy physics, condensed matter, and soft matter. Topics are

Large orders in perturbation theory, instantons, Padé and Borel resummation
Operator product expansion ; polymers and their mapping to φ4-theory
Stochastic field theory
Disordered elastic systems : metastability, non-analyticity of the effective action
Functional RG and non-perturbative RG
Avalanches and their resummation via instantons
Reaction-diffusion systems. Sandpiles, and their relation to disordered elastic systems.

Course Material

Lecture Notes. The lecture notes are provided for students of the class only. Please do not circulate. The notes contain additional material note covered in the class. Please send me any misprints you find. The part on disordered systems is with some corrections and many additional details covered in my recent review.
Movies: contact-line depinning, crack-front propagation.
Exercises: 1+2, 3, 4, 5, 6, 7, 8.
Mathematica Notebooks: Padé-Borel resummation, Random-Bond fixed point with Mathematica introduction

Lecturers

Lectures: Kay Wiese
Exercise Group: Camille Aaron