Non-constant ground configurations in the disordered Ising ferromagnet

The disordered Ising 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 a configuration of the model in infinite volume whose energy cannot be lowered by finite changes. It has been asked whether the disordered Ising ferromagnet on Z^D admits non-constant ground configurations. It is conjectured that such configurations do not exist in dimension D=2, as their existence is equivalent to the existence of bigeodesics in first-passage percolation. We prove that non-constant ground configurations do exist in dimensions D>=4 for suitable coupling constant distributions. The talk will discuss the problem and its background, and present ideas from the proof.

No previous familiarity with the topic will be assumed. This is based on joint work with Michal Bassan and Shoni Gilboa.