The long-range Ising model extends the classical Ising framework by allowing every pair of spins to interact, with interaction strength decaying polynomially in the distance between them. In one dimension, this system—often referred to as the Dyson model—exhibits spontaneous magnetization at sufficiently low temperature, a phenomenon absent in its nearest-neighbour counterpart. Another variation of the Ising model, called the random field Ising model (RFIM), incorporates an independent Gaussian random external field acting on each site. This model has garnered significant interest recently, and it is most notorious for its lack of a phase transition in two dimensions.

In this talk, I will present recent results on the existence and nature of phase transitions in the long-range RFIM. I will describe the techniques used to establish these findings and outline open problems and potential avenues for future research.

Joint work with L. Affonso, R. Bissacot, J. Ding, and F. Huang.

Biography

João Maia is a postdoctoral researcher at Peking University under the supervision of Jian Ding. He earned his Ph.D. from the University of São Paulo, working under the supervision of Rodrigo Bissacot. His research focuses on classical statistical mechanics, with particular emphasis on long-range models and systems subject to external perturbations.

Inviter: Hai-Jun Zhou