June 9, 1999

STATISTICAL MECHANICS:
CRITICAL PHENOMENA AND RENORMALIZATION THEORY
Spring quarter 1999
NU Graduate Physics Course D16-2
course schedule

Predrag Cvitanovic'

Course schedule
www.phys.nwu.edu/~predrag/NUcourses/D16-2-sched99.html
Course description
www.phys.nwu.edu/~predrag/NUcourses/D16-2-Spr99.html

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

TEXTS:

P.M. Chaikin and T.C. Lubensky, Principles of condensed matter physics (Cambridge University Press, Cambridge 1995). All chapter and exercise numbers refer to this book, unless stated otherwise.
P. Cvitanovic', Field theory, (available in parts on the web)
P. Cvitanovic', Lattice Field Theory notes

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

Place and times:TTh 12:30 - 2:00 in Tech L168


Lecture 1          12:30 - 2:00 tuesday, March 30, 1999 in Tech L168
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, April 1, 1999 in Tech L168
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, April 6, 1999 in Tech L168
Mean-field theory

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

Lecture 4           12:30 - 2:00 thursday, April 8, 1999 in Tech L168
Critical exponents

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

Lecture 5          12:30 - 2:00 tuesday, April 13, 1999 in Tech L168
Kadanoff spin-blocking

Reading: Chapter 5, sects. 5.5, 5.6

Lecture 6          12:30 - 2:00 thursday, April 15, 1999 in Tech L168
Kadanoff-Migdal construction

Reading: Chapter 5, sects. 5.5, 5.6

Lecture 7          12:30 - 2:00 tuesday, April 20, 1999 in Tech L168
Kadanoff-Migdal construction

Reading: Chapter 5, sects. 5.7, 5.8

Lecture 8           12:30 - 2:00 thursday, April 22, 1999 in Tech L168
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, April 27, 1999 in Tech L168
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, April 29, 1999 in Tech L168
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, May 4, 1999 in Tech L168
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, May 6, 1999 in Tech L168
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, May 11, 1999 in Tech L168
Title

Lecture 14          12:30 - 2:00 thursday, May 13, 1999 in Tech L168
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, May 18, 1999 in Tech L168
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, May 20, 1999 in Tech L168
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, May 25, 1999 in Tech L168
Renormalization in 3.99 dimensions

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

Lecture 18          12:30 - 2:00 thursday, May 27, 1999 in Tech L168
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, May 28.


Due 2:30 PM 12:30 PM tuesday, June 1, 1999, in my office, Tech F332, or in the class.
Reading: the whole course

Reading period starts.

Rest of the schedule is preliminary

Lecture 19          12:30 - 2:00 tuesday, June 1, 1999 in Tech L168
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, 1999 in Tech L168
Renormalization in 3.99 dimensions

We focus on Wilson's momentum space renormalization in 3.99 dimensions.
Dept. of Physics & Astronomyreturn to the Department of Physics & Astronomy.

Predrag Cvitanovic', p-cvitanovic@nwu.edu