Renormalized field theory of collapsing directed randomly branched polymers

Details Renormalized field theory of collapsing directed randomly branched polymers Renormalized field theory of collapsing directed randomly branched polymers

2009-07-20

arxiv.org/abs/0907.3430v2

Phys. Rev. E 80, 041809 (2009)

Physics

Condensed Matter

Soft Condensed Matter

18 pages, 7 figures

Scientific paper

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 $\varepsilon$-expansion that this transition belongs to the same universality class as directed percolation.

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