Course Descriptions

16:642:563 - Statistical Mechanics I: Equilibrium

Fall 2021 - Joel Lebowitz

Subtitle:

Statistical Mechanics

Course Description:

Rigorous Results in Equilibrium Statistical Mechanics

Text:

None

Prerequisites:

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Schedule of Sections:

Previous Semesters:

Fall 2017 (course was cancelled):

Joel Lebowitz

Description:

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: lebowitz@math.rutgers.edu. We can then set up a time to meet.