Directed Branched Polymer near an Attractive Line

TL;DR

This paper analyzes the adsorption-desorption phase transition of directed branched polymers near an attractive line, providing exact solutions in 1+1 dimensions, calculating crossover exponents, and deriving scaling functions for different dimensions.

Contribution

It offers the first exact solution for the model in 1+1 dimensions and extends the analysis to 2+1 dimensions, including crossover exponents and scaling functions.

Findings

Exact solution for 1+1 dimensions

Crossover exponent at the critical point

Scaling function of the sticking fraction

Abstract

We study the adsorption-desorption phase transition of directed branched polymer in $d+1$ dimensions in contact with a line by mapping it to a $d$ dimensional hard core lattice gas at negative activity. We solve the model exactly in 1+1 dimensions, and calculate the crossover exponent related to fraction of monomers adsorbed at the critical point of surface transition, and we also determine the density profile of the polymer in different phases. We also obtain the value of crossover exponent in 2+1 dimensions and give the scaling function of the sticking fraction for 1+1 and 2+1 dimensional directed branched polymer.