Surface crossover exponent for branched polymers in two dimensions

TL;DR

This paper uses transfer-matrix methods on finite-width strips to estimate the crossover exponent for branched polymers in two dimensions, confirming the theoretical value of 1/2.

Contribution

It provides a numerical estimate of the crossover exponent for branched polymers in two dimensions, supporting the conjecture that it equals 1/2 across all dimensions.

Findings

Crossover exponent estimated as φ = 0.505 ± 0.015

Results are consistent with the conjecture φ = 1/2

Method applied to lattice site animals in good solvent

Abstract

Transfer-matrix methods on finite-width strips with free boundary conditions are applied to lattice site animals, which provide a model for randomly branched polymers in a good solvent. By assigning a distinct fugacity to sites along the strip edges, critical properties at the special (adsorption) and ordinary transitions are assessed. The crossover exponent at the adsorption point is estimated as $\phi = 0.505 \pm 0.015$, consistent with recent predictions that $\phi = 1/2$ exactly for all space dimensionalities.