Fall 2026
Joel Lebowitz
Course Description:
Rigorous result in Statistical mechanics.
Text:
None
Prerequisites:
Consent of instructor
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Fall 2025
Joel Lebowitz
Course Description:
Rigorous result in Statistical mechanics.
Gibbs measures,
Phase transitions
Text:
None
Prerequisites:
Approval of instructor
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Fall 2023
Ian Jauslin
Course Description:
Statistical mechanics is the study of macroscopic observables from a microscopic point of view. In this course, we will first discuss the foundations of equilibrium statistical mechanics, and define the relevant mathematical concepts used in the field. We will then put these to good use by studying a variety of systems and phenomena.
Text:
Statistical Mechanics of Lattice Systems: a Concrete Mathematical Introduction, by Friedli and Velenik (freely available on https://www.unige.ch/math/folks/velenik/smbook/)
Prerequisites:
Basics in probability theory and analysis
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Fall 2022
Joel Lebowitz
Subtitle:
Statistical Mechanics
Course Description:
Rigorous Results in Equilibrium Statistical Mechanics
Thermodynamic Limit, Phase transitions
Text:
None
Prerequisites:
Talk with me
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Fall 2021
Joel Lebowitz
Subtitle:
Statistical Mechanics
Course Description:
Rigorous Results in Equilibrium Statistical Mechanics
Text:
None
Prerequisites:
Talk with me
Schedule of Sections:
Previous Semesters:
- Fall 2020 Prof. Lebowitz
- Fall 2019 Prof. Lebowitz
- Fall 2018 Prof. Goldstein
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: . We can then set up a time to meet.