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).
João Rodrigues Pereira and Kelvyn Welsh:
- 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:
Random Currents - João Vitor Maia
Peierls Bound - Lucas Affonso
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).