Department of Physics Papers

Document Type

Journal Article

Date of this Version

10-30-2009

Comments

Suggested Citation:
Janssen, H., Wevelsiep, F. and Stenull, O. (2009). "Renormalized field theory of collapsing directed randomly branched polymers." Physical Review E. 80, 041809.

© 2009 The American Physical Society
http://dx.doi.org/10.1103/PhysRevE.80.041809

Abstract

We present a dynamical field theory for directed randomly branched polymers and in particular their collapse transition. We develop a phenomenological model in the form of a stochastic response functional that allows us to address several interesting problems such as the scaling behavior of the swollen phase and the collapse transition. For the swollen phase, we find that by choosing model parameters appropriately, our stochastic functional reduces to the one describing the relaxation dynamics near the Yang-Lee singularity edge. This corroborates that the scaling behavior of swollen branched polymers is governed by the Yang-Lee universality class as has been known for a long time. The main focus of our paper lies on the collapse transition of directed branched polymers. We show to arbitrary order in renormalized perturbation theory with ε expansion that this transition belongs to the same universality class as directed percolation.

 

Date Posted: 21 December 2010

This document has been peer reviewed.