On the phase diagram of the polymer model

2024/02/19 by Krishnan, Arjun, Mkrtchyan, Sevak, Neville, Scott
#60K35 #60K37 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2402.12580

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.

Related

• Non-directed polymers in random environments with range penalties: the high dimensional case
• Directed polymers in a random environment: a review of the phase transitions
• The high-temperature behavior for the directed polymer in dimension 1+2
• Continuous Model for Homopolymers
• Asymmetry in Polymer-Solvent Interactions Yields Complex Thermoresponsive Behavior