June 9, 2006

CRITICAL PHENOMENA AND RENORMALIZATION THEORY
fall semester 2006
GT PHYS-8803
course schedule

Predrag Cvitanovic'

Course schedule
www.cns.gatech.edu/~predrag/courses/PHYS-8803-06/syllabus.html

For people following the course, check the e-mail list.

TEXTS:

Leo P. Kadanoff, Statistical Physics: Statics, Dynamics and Renormalization (World Scientific, Singapore 2000). All chapter and exercise numbers refer to this book, unless stated otherwise.
P. Cvitanovic', Field theory webbook
P. Cvitanovic', Quantum Field Theory lecture notes

I would like to receive solutions to problem sets by Tuesday, at the lecture, or in my mailbox, School of Physics.


Place and times:Tue, Thu 09:35-10:55 in Howey W505 (tentative - can be changed to avoid class conflicts)



Lecture 1           09:35-10:55 tuesday, Aug 22, 2006 in Howey W505
Rest of the schedule is preliminary
Preliminaries I

We start by reviewing order paramenters, Bragg-Williams theory, phase transitions, critical exponents, mean-field theory, Landau theory, Ising models, variational mean-field theory

Reading: chapter 4, sects. 4.1, 4.2, 4.3, 4.8.1-4.8.4
Problems: at least 4.9

Lecture 2          12:30 - 2:00 thursday, Sep 1, 2006 in Howey W505
Preliminaries II
(continued)
Reading: chapter 4, sects. 4.1, 4.2, 4.3, 4.8.1-4.8.4
Problems: at least 4.9

Lecture 3          12:30 - 2:00 tuesday, Sep 6, 2006 in Howey W505
Mean-field theory


Reading: chapter 5, sects. 5.1, 5.2, 5.3
Problems: at least

Lecture 4           12:30 - 2:00 thursday, Sep 8, 2006 in Howey W505
Critical exponents


Reading: chapter 5, sect. 5.4
Problems: at least

Lecture 5          12:30 - 2:00 tuesday, Sep 13, 2006 in Howey W505
Kadanoff spin-blocking


Reading: Chapter 5, sects. 5.5, 5.6

Lecture 6          12:30 - 2:00 thursday, Sep 15, 2006 in Howey W505
Kadanoff-Migdal construction


Reading: Chapter 5, sects. 5.5, 5.6

Lecture 7          12:30 - 2:00 tuesday, Sep 20, 2006 in Howey W505
Kadanoff-Migdal construction


Reading: Chapter 5, sects. 5.7, 5.8

Lecture 8           12:30 - 2:00 thursday, Sep 22, 2006 in Howey W505
Title  

We will focus on lattice field theory, discrete Fourier transfomrs.


Reading: P. Cvitanovic' Field theory, chapter 5
Problems: at least prove tr log = log det, problem 2

Solution to the tr log = log det problem, from M. Veltman, Diagrammatica: The Path to Feynman Diagrams (Cambridge U. Press, 1994)

Lecture 9          12:30 - 2:00 tuesday, Sep 27, 2006 in Howey W505
Perturbative lattice field theory



Reading:
P. Cvitanovic' Lattice Field Theory notes. They are not finished yet, so you might not want to print them on paper yet.
P. Cvitanovic' Field theory, chapter 3, sections 3.B, 3.C,

Problems: 3.B.1 on page 36.

Lecture 10          12:30 - 2:00 thursday, Sep 29, 2006 in Howey W505
Asymptotic expansions

Saddle point expansions, phi-4 perturbative corrections.


Reading:
Intro to Dingle monograph Asymptotics - A Behavioural Survey pp. 1-4.
Problems:

Lecture 11           12:30 - 2:00 tuesday, Oct 4, 2006 in Howey W505
Feynman diagrams

Reading:
P. Cvitanovic' Lattice Field Theory notes. Current version is still not final (!), but read it anyway, do the problems (in particular, the one on phi^4 asymptotics).

Lecture 12          12:30 - 2:00 thursday, Oct 6, 2006 in Howey W505
Functional integrals in Fourier space

Reading:
P. Cvitanovic' Field theory, chapter 2. I do not mean that you should really work through this - it is too much field theory for our goals in this course, but there are a few point that might be of interest:

Section 2.F purports to relate full and connected Green functions in a few lines. Many books work do this via painful combinatoric proofs which seem pointless and not very bright to me, so let me know if there is a hole in my derivation.
Exercise 2.D.1 defines Quantum Electro Dynamics notation that I forgot to explain in exercise 3.F.3. I gave you this exercise to treat diagrams that one runs into always in condensed matter physics (particle-hole exciations, etc).

Problems: do the current set from the Lattice Field Theory notes.

Lecture 13          12:30 - 2:00 tuesday, Oct 11, 2006 in Howey W505
Title

Lecture 14          12:30 - 2:00 thursday, Oct 13, 2006 in Howey W505
Ising model - real space renormalization

We focus on the Kadanoff renormalization intuition.

Problems: 1 and 2-d Ising model real space renormalization

Lecture 15          12:30 - 2:00 tuesday, Oct 18, 2006 in Howey W505
Title  


Reading: chapter 10, sects. 10.1, 10.2, 10.4,
Problems: at least 10.6, 10.9

Lecture 16          12:30 - 2:00 thursday, Oct 20, 2006 in Howey W505
Renormalization in 3.99 dimensions

We focus on Wilson's momentum space renormalization in 3.99 dimensions.

Reading: C Jayaprakash's 4-d dimension renormalization on three sheets of paper

Lecture 17          12:30 - 2:00 tuesday, Oct 25, 2006 in Howey W505
Renormalization in 3.99 dimensions

We focus on Wilson's momentum space renormalization in 3.99 dimensions.

Lecture 18          12:30 - 2:00 thursday, Oct 27, 2006 in Howey W505
Renormalization in 3.99 dimensions

We focus on Wilson's momentum space renormalization in 3.99 dimensions.

Download the final exam .

A small project-length problem will be ready on this homepage morning of Friday, Oct 28.


Due 2:30 PM 12:30 PM tuesday, June 1, 2006, in my office, Tech F332, or in the class.
Reading: the whole course

Reading period starts.

Lecture 19          12:30 - 2:00 tuesday, June 1, 2006 in Howey W505
Renormalization in 3.99 dimensions

We focus on Wilson's momentum space renormalization in 3.99 dimensions.

Lecture 20 (the last of the course)         12:30 - 2:00 thursday, June 3, 2006 in Howey W505
Renormalization in 3.99 dimensions

We focus on Wilson's momentum space renormalization in 3.99 dimensions.

Predrag Cvitanovic'