Tue, 06 Feb 2024
16:00 - 17:00
Michal Bassan
University of Oxford
The disordered ferromagnet is a disordered version of the ferromagnetic Ising model in which the coupling constants are quenched random, chosen independently from a distribution on the non-negative reals. A ground configuration is an infinite-volume configuration whose energy cannot be reduced by finite modifications. It is a long-standing challenge to ascertain whether the disordered ferromagnet on the Z^D lattice admits non-constant ground configurations. When D=2, the problem is equivalent to the existence of bigeodesics in first-passage percolation, so a negative answer is expected. We provide a positive answer in dimensions D>=4, when the distribution of the coupling constants is sufficiently concentrated.

The talk will discuss the problem and its background, and present ideas from the proof. Based on joint work of with Shoni Gilboa and Ron Peled.
Please contact us with feedback and comments about this page. Last updated on 06 Feb 2024 12:44.