PHY831 - Graduate Statistical Mechanics

Lectures MWF 10:20-11:10, BPS1308
Helproom Tuesdays 6-7:15pm, BPS1308
  • Professor Phillip Duxbury: Office: BPS 4260, Email: duxbury at pa.msu.edu

    Active lecture notes and problems sets.

    Complete Lectures Notes for Part 4
    Solutions to quiz and assigned problems for Part 4
    Midterm IV and solutions

    Upcoming exams, quizzes, homeworks

    Exam/Quiz/Assignment schedule

    Assignment 4.1 Due Monday Dec. 5. Assigned Problems: 1, 2, 4, 6, 7
    Midterm 4, Lecture 41 (Wednesday Dec. 7 - 30 minute exam)
    Final (Statistical Mechanics Subject Exam), Wednesday Dec. 14, 10:00am - 1pm, BPS 1400.
    The final will cover all material, except the RG and dynamics sections after the RG in the notes
    Draft of Subject Exam Cover Sheet
    Subject Exam and Solutions

    Course schedule and outline

    Part 1: (LL, PB) Foundations: (10 lectures)
    History, Heat, Engines, Kinetic theory and Entropy. Computational methods, molecular dynamics, ensembles, ergodicity. Foundations of Equilibrium Statistical Mechanics. Ensembles, Boltzmann factors, Quantum systems. Computational methods, Monte Carlo and detailed balance. Free energies and thermodynamics. Fun with thermodynamic relations. Fluctuations and response functions. Equilibrium and Non-equilibrium Dynamics.
    Lecture notes, solutions and midterm for Part 1
    Complete lecture notes for Part 1
    Solutions to quiz and assigned problems for Part 1
    Midterm I and solutions


    Part 2: (H, PB, LL) Key solvable systems: (10 lectures)
    Non-interacting spin systems. Ideal Classical gas. Classical harmonic oscillators. Ideal Fermi gas, electron gas, white dwarf stars. Ideal Bose gas, photons, phonons, bose condensation, The early universe. Electrons and phonons in metals. Solvable Ising systems. Magnetic properties of the electron gas.
    Complete lecture notes for Part 2
    Solutions to quiz and assigned problems for Part 2
    Midterm II and solutions

    Part 3: (H, PB) Interacting systems, phase transitions and critical phenomena (9 lectures)
    Interacting spin systems, Ising model. Interacting classical gas, cluster expansion, van der Waals gas, virial Expansion. BCS model of superconductivity.
    Complete lecture notes for Part 3
    Solutions to quiz and assigned problems for Part 3
    Midterm III and Solutions


    Part 4: (H, PB) Scaling and complex systems (9 lectures)
    Landau theory of phase transitions and critical phenomena, scaling. GL theory, RG. Equilibrium and non-equilibrium dynamics. Fractals, percolation, DLA, self-organized criticality, scale free networks.
    Midterm 4, Lecture 42 (Friday Dec. 9)

    Books and other resources

    There is no graduate level Statistical Mechanics text that covers the above material in a clean and pedagogical way. Landau and Lifshitz, volume 1 and Pathria and Beale are best for Part 1, Huang for Parts 2-4. Some parts of Part 4 are not in any of these texts. In any case it is a good idea to work through at least two texts, and for that I suggest PB and H. Hopefully everyone has worked through a book such as LL in an undergraduate statistical mechanics course.
    Recommended text(PB): R.K. Pathria and P.D. Beale, Statistical Mechanics Third Edition 2011
    Recommended text(H): K. Huang, Statistical Mechanics, Second Edition 1987
    Recommended but lower level(LL): Statistical Physics, L.D. Landau and E.M. Lifshitz
    Recommended but lower level: Thermal Physics, C. Kittel and H. Kroemer
    Problems and solutions: Statistical Mechanics, R. Kubo
    Professor Scott Pratt has a PHY831 www site that is a good resource for PHY831 problems, past subject exams and his lecture notes.
    Professor Steven Teitel has a nice set of notes and problems with solutions.

    Course assessment

    Weekly or biweekly homeworks (10%). Hand in a copy of your work, not the original. Late homeworks will not be accepted without a written explanation.
    Quizzes (random, almost weekly) (20%). Your worst quiz will be dropped.
    Midterms (40%). Final (30%).