Branched polymers on the two-dimensional square lattice with attractive surfaces

Using the renormalization group approach, an analysis is given of the asymp totic properties of branched polymers situated on the two-dimensional squar e lattice with attractive impenetrable surfaces. We modeled branched polyme rs as site lattice animals with loops and site lattice animals without loop s on the simple square lattice. We found the gyration radius critical expon ent nu = 0.6511 +/- 0.0003 and nu = 0.6513 +/- 0.0003 for branched polymers with and without loops, respectively. Our results for the crossover expone nt phi = 0.502 +/- 0.003 for branched polymers with loops and phi = 0.503 /- 0.003 for branched polymers without loops satisfy the recent hyperuniven sality conjecture phi = 1/2 In addition, we have studied partially directed site lattice animals.