Speaker: Rafael Greenblatt

Title:
Non-solvable Ising-like models and the constructive renormalization group

Abstract:
The planar Ising model is one of the best-known exactly solved models in statistical mechanics, however many important properties which have been shown using the exact solution (like conformal invariance of the scaling limit) should apply to a broader class of (generically non-solvable) models obtained by perturbing the Hamiltonian with an arbitrary finite-range term which respects the symmetries of the model.  

Some rigorous results in this direction have been obtained using constructive renormalization group methods originally developed for the study of interacting Fermionic quantum field theories.  I will present a recent result on energy correlations on the discrete cylinder, obtained in a joint work with G. Antinucci and A. Giuliani (arXiv:2006.04458), and discuss the prospects of further results.