PY 895 RG and Disorder, Fall 2024

This is the website for PY 895, Advanced Topics in Statistical Physics: Disordered Systems and the Renormalization Group. This website will be updated with scanned hand written lecture notes and homework assignments.

General course information:
We meet TH 9:30-10:45 in PRB 148.
Office hours Th 11-noon in SCI 323

Syllabus pdf .

Textbooks worth reading:

Renormalization Group:

Creswick, Richard J., Horacio A. Farach, and Charles P. Poole. Introduction to renormalization group methods in physics (out-of-print) but pdfs are floating around on internet. Please contact me in class if you have trouble locating one.
Cardy, John. Scaling and renormalization in statisticalphysics. Vol. 5. Cambridge university press, 1996.
Goldenfeld, Nigel. Lectures on phase transitions and the renormalization group . CRC Press, 2018.
Kadanoff, Leo P. Statistical physics: statics, dynamics and renormalization. World Scientific, 2000.

Disordered Systems

Mézard, Marc, Giorgio Parisi, and Miguel Angel Virasoro. Spin glass theory and beyond: An Introduction to the Replica Method and Its Applications. Vol. 9. World Scientific Publishing Company, 1987.
Nishimori, Hidetoshi. Statistical physics of spin glasses and information processing: an introduction. No. 111. Clarendon Press, 2001.
Amit, Daniel J., and Daniel J. Amit. Modeling brain function: The world of attractor neural networks. Cambridge university press, 1989.
Mezard, Marc, and Andrea Montanari. Information, physics, and computation. Oxford University Press, 2009.
Stein, Daniel L. and Newman, Charles M. Spin Glasses and Complexity. Princeton University Press, 2013.

Homeworks

Homework 1 pdf. Due Sept 17.

Homework 2 pdf. Due Oct 1.

Homework 3 pdf. Due Nov 5.

Homework 4 pdf. (Updated with some typos fixed. More remain, please report any you see). Due Nov 26.

Readings and notes

Weeks 1:

Readings:

Michael Fisher Renormalization group theory: Its basis and formulation in statistical physics. Rev. Mod Phys. 1998. A historical and philosophical overview of RG from one of the OGs of the field based on lectures given at BU. It's rather technical despite claiming otherwise. Do not expect to understand all (or even most) of it.
Creswich Chapter 1.

Notes:

Lecture 1: RG from space
Lecture 2: RG of Random Walks I

Weeks 2:

Readings:

Creswick Chapter 1, Sections 3.6, 3.7

Notes:

Lecture 3: RG of RW and SAW
Lecture 4: RG of Sol-Gel Transition

Weeks 3:

Readings:

Creswick: 3.6, 3.7. Chapter 2; Strogatz Non-linear Dynamics and Chaos 3rd edition, Chapter 10

Notes:

Lecture 4: RG of Sol-Gel Transition
Lecture 5: RG of Period Doubling Transition to Chaos

Weeks 4:

Readings:

Shankar Quantum Field Theory and Condensed Matter: An Introduction Chapter 12.
Goldenfeld Chapters 7,8
Optional: Landau's original phase transition paper (really worth reading!).

Notes:

Lecture 6: Scaling Concepts I

Weeks 5:

Readings:

Shankar Quantum Field Theory and Condensed Matter: An Introduction Chapter 12.
Creswick Chapter 4.
Widom's classic 1965 scaling paper.

Notes:

Lecture 7: Scaling Concepts II

Weeks 6:

Readings:

Chaikin and Lubensky Principles of Condensed Matter Physics Sections 5.5-5.8.
Shankar Quantum Field Theory and Condensed Matter: An Introduction Chapter 12.
Creswick Sections 5.1-5.2, 7.1-7.3, 8.7
Kadanoff Chapter 12-14

Notes:

Lecture 8: Real-space RG of Ising Model
Lecture 9: Momentum space RG I: Gaussian Fixed Point

Weeks 7-8:

Readings:

Chaikin and Lubensky Principles of Condensed Matter Physics Sections 5.5-5.8.
Shankar Quantum Field Theory and Condensed Matter: An Introduction Chapter 12.
Creswick Sections 5.1-5.2, 7.1-7.3, 8.7
Kadanoff Chapter 12-14

Notes:

Lecture 10: Momentum space RG II: Epsilon Expansion

Weeks 9:

Readings:

Mile Stoudenmire excellent directory of resources. Highlights include: the video lectures of Garnet Chan, video lectures of Uli Schollwoeck, and 1.5 hour tutorial by Miles available here; Also recommended are Uli Schollwoeck (DMRG in the Age of Matrix Product States).
We will follow these paper in class on Entanglement Renormalization and this and briefly discuss this paper.

Notes:

Lecture 11: Advanced methods: Entanglement Renormalization
Special Halloween guest lecture by Miles Stoudenmire.

Weeks 10:

Readings:

Lubchenko and Wolynes review of structural glasses

Notes:

Lecture 11 Overview of Disordered Systems
Lecture 12 Technical Tools I

Weeks 11:

Readings:

Les Houches Lectures on Ecology Chapter 8
Potters and Bouchard. A First Course in Random Matrix Theory (Chapters 1-4)

Notes:

Lecture 13 Technical Tool 2: Resolvents and RMT
Lecture 14 Generalize Lotka-Volterra and RS Breaking

Weeks 12:

Readings:

Papers on DMFT of GLV in RS-broken phase PRX and arXiv.

Notes:

Lecture 15 DMFT of GLV

Weeks 13:

Readings:

Nishimori Statistical physics of spin glasses and information processing: an introduction, Chapter 2, 3.
Mezard and Montanari Information, physics, and computation, Chapter 14.

Notes:

Lecture 16 SK-Model: overview, phase diagram, and cavity

Weeks 14:

Readings:

Mezard and Montanari Information, physics, and computation, Chapter 14.
Krzakala Lectures Belief Propagation for the (physicist) layman .
Nishimori Statistical physics of spin glasses and information processing: an introduction, Chapter 2, 3.

Notes:

Lecture 17 Introduction to Belief Propagation