Lucas Affonso

I am a Postdoc at the Institute of Mathematics and Statistics from the University of São Paulo, under the supervision of Professor Anatoli Imbartsev. During the year 2026, I will be a visiting postdoctoral researcher at NYU Shanghai, under supervision of Professor Roberto Fernández.

My main research interests are Quantum and Classical Statistical Mechanics. If you want to contact me, please send an email to lucas.affonso.pereira(at)gmail.com.

Research

Interests

My research interests lie in phase transitions of spin systems, both classical and quantum. During my Ph.D., I investigated multidimensional long-range Ising spin systems, introducing a novel contour construction better suited for a direct proof of phase transition. This approach builds upon the Fröhlich-Spencer multiscale contour method for one-dimensional long-range Ising models. Additionally, during a one-year visit to the University of Victoria, my coauthors and I developed a specification theory applicable to a broad class of quantum spin systems. This framework facilitates the formulation of a general DLR (Dobrushin-Lanford-Ruelle) approach to equilibrium states in quantum spin systems. Below is an up-to-date list of my coauthors.

Coauthors

Publications

  1. Cluster Expansion and Decay of Correlations for Multidimensional Long-Range Ising Models

    joint with Rodrigo Bissacot, João Maia, João F. Rodrigues, and Kelvyn Welsch - Submitted

  2. Phase Transitions on 1d Long-Range Ising Models with Decaying Fields: A Direct Proof via Contours

    joint with Rodrigo Bissacot, Henrique Corsini, and Kelvyn Welsch -

  3. Phase Transition in Ferromagnetic $q$−state Models: Contours, Long-Range Interactions and Decaying Fields

    joint with Rodrigo Bissacot, Gilberto Faria, and Kelvyn Welsch - Submitted

  4. Phase Transitions in Multidimensional Long-Range Random Field Ising Models

    joint with Rodrigo Bissacot, and João Maia - Submitted

  5. Quantum Statistical Mechanics via Boundary Conditions. A Groupoid Approach to Quantum Spin Systems

    joint with Rodrigo Bissacot, and Marcelo Laca

  6. Long-Range Ising Models: Contours, Phase Transitions and Decaying Fields

    joint with Rodrigo Bissacot, Eric O. Endo, and Satoshi Handa - J. Eur. Math. Soc.27 (2025), no. 4, pp. 1679–1714

Teaching

Course
Poisson Point Processes in Statistical Mechanics CV
Long range Ising model- Phase transition and multiscale methods CV
T.A. for C* algebras and Quantum Gibbs States CV
T.A. for An Introduction to Ergodic Theory CV

Miscellaneous

Under Construction!