When
3 – 4 p.m., Oct. 16, 2024
In dimension 1, the directed polymer model is in the celebrated KPZ
universality class, and for all positive temperatures, a typical polymer path
shows non-Brownian KPZ scaling behavior. In dimensions 3 or larger, it is a
classical fact that the polymer has two phases: Brownian behavior at high
temperature, and non-Brownian behavior at low temperature. We consider the
response of the polymer to an external field or tilt, and show that at fixed
temperature, the polymer has Brownian behavior for some fields and non-Brownian
behavior for others. In other words, the external field can *induce* the phase
transition in the directed polymer model.
(joint work with S. Mkrtchyan and S. Neville)