Gibbs 2021

Official webpage of this course at the University of São Paulo. (in Portuguese)

Classes: Tuesday 16:00 - 18:00

Thursday 16:00 - 18:00

Room: Zoom

Teacher Assistant: João Vitor Maia - joao.vitor.maia@usp.br

Papers to students:

  • Henrique Corsini:

- Random Surfaces. By Scott Sheffield. Asterisque 2005, No. 304

- Gibbs measures on Subshifts. by Bruno Kimura, 2015.

  • Gustavo Oshiro de Carvalho:

- A New Correlation Inequality for Ising Models with External Fields. By Jian Ding, Jian Song, Rongfeng Sun, 2021.

  • Leonardo Teramatsu and Alan Ramer:

- On the uniqueness of the Invariant Equilibrium State and surface tension. By C. Gruber, A. Hintermann, A. Messager & S. Miracle-Sole Communications in Mathematical Physics 56, pages147–159 (1977).

  • Sergio Noboru Yuzuka and Julian Lazaro Aguirre:

- Surface tension and phase transition for lattice systems. By J. R. Fontaine & Ch. Gruber. Communications in Mathematical Physics 70, pages 243–269 (1979).

- Marginal triviality of the scaling limits of critical 4D Ising and $\varphi_4^4$ models. By M. Aizenman and Hugo Duminil-Copin. Annals of Mathematics 2021+.


Extra Topics:


Books, thesis, and lectures notes:

- Probability measures on metric spaces. Onno van Gaans, (2002/2003).

- Statistical Mechanics of Lattice Systems: A Concrete Mathematical Introduction. Sacha Friedli and Yvan Velenik. Cambridge University Press, (2017).

- Statistical Mechanics of Disorder Systems - A Mathematical Perspective. Anton Bovier. Cambridge Series in Statistical and Probabilistic Mathematics, (2006).

- A Course on Large Deviations with an Introduction to Gibbs Measures. Firas Rassoul-Agha and Timo Seppalainen, (2010).

- Statistical Mechanics: Rigorous Results. David Ruelle. World Scientific, (1999).

- Gibbs Measures and Phase Transitions(Second Edition). Hans-Otto Georgii. De Gruyter Studies in Mathematics; 9. Walter de Gruyter & Co; (2011).

- Introduction to (generalized) Gibbs Measures. Arnaud Le Ny. Ensaios Matemáticos. Vol. 15, 1-126. SBM, (2008).

- Entropy, Large Deviations, and Statistical Mechanics. Richard S. Ellis. Classics in Mathematics. Springer-Verlag, (2006).

- The statistical mechanics of lattice gases. B. Simon. Vol. I. Princeton Series in Physics. Princeton University Press, Princeton, NJ, (1993).

- Quantum Physics: A Functional Integral Point of View. J. Glimm & A. Jaffe. Springer-Verlag, (1981).

- Interacting particle systems on graphs. Nazim Hikmet Tekmen. PhD thesis, Bielefeld University, (2010).

- Convexity in the Theory of Lattice Gases. Robert B. Israel. Princeton University Press, (1979).

- Introdução a Teoria das Medidas de Gibbs. Rodrigo Bissacot e Leandro Cioletti. Notas de aula, (2012).

- Group Analysis of Classical Lattice Systems. C. Gruber, A. Hintermann, D. Merlini. Lecture Notes in Physics (1977).

- Scaling Limits in Statistical Mechanics and Microstructures in Continuum Mechanics. Errico Presutti, (2008).