On the phase diagram of branched polymer collapse

TL;DR

This paper explores the phase diagram of two-dimensional branched polymers, revealing multiple transition lines and universality classes, with exact solutions and renormalization group analysis.

Contribution

It provides an exact solution for the phase diagram of branched polymers using Bethe lattice and Migdal-Kadanoff methods, identifying multiple transition lines and universality classes.

Findings

Existence of a line of $ heta$ transitions with different universality classes.

Identification of a multicritical point where transition lines meet.

Directed branched polymers have a single $ heta$ transition in the directed percolation class.

Abstract

The phase diagram of the collapse of a two-dimensional infinite branched polymer interacting with the solvent and with itself through contact interactions is studied from the $q\to 1$ limit of an extension of the $q-$ states Potts model. Exact solution on the Bethe lattice and Migdal-Kadanoff renormalization group calculations show that there is a line of $\theta$ transitions from the extended to a single compact phase. The $\theta$ line, governed by three different fixed points, consists of two lines of extended--compact transitions which are in different universality classes and meet in a multicritical point. On the other hand, directed branched polymers are shown to be completely determined by the strongly embedded case and there is a single $\theta$ transition which is in the directed percolation universality class.