Surface crossover exponent for branched polymers in two dimensions

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 φ = 0.505 ± 0.015, consistent with recent predictions that φ = 1/2 exactly for all space dimensionalities.