English

On the phase diagram of the polymer model

Probability 2025-04-15 v2 Mathematical Physics math.MP

Abstract

In dimensions 3 or larger, it is a classical fact that the directed polymer model 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.

Keywords

Cite

@article{arxiv.2402.12580,
  title  = {On the phase diagram of the polymer model},
  author = {Arjun Krishnan and Sevak Mkrtchyan and Scott Neville},
  journal= {arXiv preprint arXiv:2402.12580},
  year   = {2025}
}

Comments

33 pages; version 2 with an updated result for the discrete Gaussian walk