Welcome to Exactly solvable models in statistical mechanics, a course hosted by the Taught Course Center of Bath-Bristol-Imperial-Oxford and Warwick. This page summarizes all key information of the module and contains all course materials, most importantly our weekly schedule.
Key organizational information:
Instructor: Thomas Bothner
Office: 2A.15, Fry Building (not during COVID-19 lockdowns)
Contact: thomas.bothner@bristol.ac.uk and 0117 428 4992
Meeting times: Thursdays 1:30-3:30pm starting April 29th, 2021 via Microsoft TEAMS
This course is suitable for students interested in mathematical statistical mechanics, in particular students interested in the theory of lattice spin systems. We will address several fundamental concepts of the theory through the analysis of selected models. Topics will include
The Curie-Weiss model (thermodynamic limit and critical exponents)
The Ising model (van Hove theorem, infinite-volume Gibbs states, correlation inequalities, phase diagram, Peierls' argument, Lee-Yang theorem, Kramers-Wannier duality)
The Gaussian free field (infinite-volume Gibbs states, random walk representation)
Models with continuous symmetry (Mermin-Wagner theorem)
There is no exam for this course. If you are taking the module for credit you must complete the posted exercises and email me your solutions in LaTeX typeset by the due date written on the exercise sheet.
This course is offered exclusively to PhD students and Postdocs at the Universities of Bath, Bristol, Oxford, Warwick and Imperial College London. If you are eligible and interested in this course please sign up via gradstud@maths.ox.ac.uk or contact me directly if there are any issues. The course will run for 8 consecutive weeks, see the weekly schedule below.
Course materials (click the links):
Welcome to Exactly solvable models in Statistical mechanics - Introductory slides
Lecture Notes (June 17th, 2021 version - let me know about typos)
Exercises (June 10th, 2021 version)
Weekly schedule:
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Week 1, April 29th, 2021 from 1:30-3:30pm Bristol time:
Topics: Overview, Curie-Weiss model (definition, thermodynamic limit)
Materials: Lesson Notes
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Week 2, May 6th, 2021 from 1:30-3:30pm Bristol time:
Topics: Curie-Weiss model (critical exponents), Ising model (definition, thermodynamic limit)
Materials: Lesson Notes
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Week 3, May 13th, 2021 from 1:30-3:30pm Bristol time:
Topics: Ising model (one-dimensional model, infinite-volume Gibbs states, correlation inequalities)
Materials: Lesson Notes
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Week 4, May 20th, 2021 from 1:30-3:30pm Bristol time:
Topics: Ising model (infinite-volume Gibbs states, phase diagram, low-temperature representation)
Materials: Lesson Notes
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Week 5, May 27th, 2021 from 1:30-3:30pm Bristol time:
Topics: Ising model (Peierls argument, high-temperature representation, Lee-Yang theory)
Materials: Lesson Notes
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Week 6, June 3rd, 2021 from 1:30-3:30pm Bristol time:
Topics: Ising model (Lee-Yang circle theorem), Gaussian free field (definition)
Materials: Lesson Notes
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Week 7, June 10th, 2021 from 1:30-3:30pm Bristol time:
Topics: Gaussian free field (harmonic functions, random walk representation, massive field)
Materials: Lesson Notes
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Week 8, June 17th, 2021 from 1:30-3:30pm Bristol time:
Topics: Models with continuous symmetry (definition, Mermin-Wagner theorem)
Materials: Lesson Notes