Ferromagnets have the following response to an external magnetic field: When the temperature is higher than the critical temperature (Tc), the fraction of microscopic spins in the ferromagnetic material aligned with the external magnetic field is proportional to the strength of the magnetic field. However, when the temperature is below Tc, almost all the spins will align completely with the external magnetic field, whatever its strength. This is a classical example of a phase transition.

We consider a similar phase transition in the standard directed polymer model. In dimension 1, the polymer model is in the celebrated KPZ universality class. In dimensions strictly greater than 2, 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, 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)