Rodrigo Bissacot (University of São Paulo (USP), Brazil)  
Title: Ferromagnetic Ising models with decaying fields.
Abstract: Ising models with decaying fields are examples of models where phase transitions (in terms of the number of DLR states)
are not detected by the pressure (free energy) function. The models have the same pressure function as the model with
zero magnetic field, but the set of Gibbs measures is different depending on the decay of the field. After a brief review of some
results about this class of models, we will concentrate the discussion on a recent result about the multidimensional ferromagnetic long-range
Ising model. Inspired by Fröhlich-Spencer and subsequent authors we introduced a notion of contour for long-range systems, and we provide 
a direct proof for the phase transition at low temperatures. The argument, which is based on a multi-scale analysis, is sharp with respect to the exponent
of the interaction for the zero-field case and improves previous results obtained by Park, and by Ginibre, Grossmann, Ruelle. 
We prove the persistence of the phase transition when we add a magnetic field decaying fast enough, which we believe is also sharp for the 
phase transition problem when we have a decaying field. Jointly work with Lucas Affonso (USP, Brazil/Uvic, Canada), Eric Endo (NYU-Shanghai, China)
and Satoshi Handa (Hokkaido University, Japan), available at arXiv:2105.06103.