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Course Descriptions

16:642:563 - Statistical Mechanics I: Equilibrium

Joel Lebowitz




The course will cover traditional areas of statistical mechanics with a mathematical flavor. It will describe exact results where available and heuristic physical arguments where applicable. A rough outline is given below:

I. Overview: microscopic vs. macroscopic descriptions; microscopic dynamics and thermodynamics.

II. Energy surface; microcanonical ensemble; ideal gases; Boltzmann’s entropy, typicality.

III. Alternate equilibrium ensembles; canonical, grand-canonical, pressure, etc. Partition functions and thermodynamics.

IV. Thermodynamic limit; existence; equivalence of ensembles; Gibbs measures.

V. Cooperative phenomena: phase diagrams and phase transitions; probabilities, correlations and partition functions. Law of large numbers, fluctuations, large deviations.

VI. Ising model, exact solutions. Griffith’s, FKG and other inequalities; Peierle’s argument; Lee-Yang theorems.

VII. High temperature; low temperature expansions; Pirogov-Sinai theory.

VIII. Fugacity and density expansions.

IX. Mean field theory and long range potentials.

X. Approximate theories: integral equations, Percus-Yevick, hypernetted chain. Debye-Hückel theory.

XI. Critical phenomena: universality, renormalization group.

XII. Percolation and stochastic Loewner evolution.

If you have any questions about the course please email me: We can then set up a time to meet.

Sections Taught This Semester:

For more information on instructors and sections for this course, please see our Teaching Schedule Page

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Department of Mathematics

Department of Mathematics
Rutgers University
Hill Center - Busch Campus
110 Frelinghuysen Road
Piscataway, NJ 08854-8019, USA

Phone: +1.848.445.2390
Fax: +1.732.445.5530