Branched Polymers on the Two-Dimensional Square Lattice with Attractive Surfaces

Abstract

Using the renormalization group approach, an analysis is given of the asymptotic properties of branched polymers situated on the two-dimensional square lattice with attractive impenetrable surfaces. We modeled branched polymers as site lattice animals with loops and site lattice animals without loops on the simple square lattice. We found the gyration radius critical exponent ν=0.6511±0.0003 and ν=0.6513±0.0003 for branched polymers with and without loops, respectively. Our results for the crossover exponent φ=0.502±0.003 for branched polymers with loops and φ=0.503±0.003 for branched polymers without loops satisfy the recent hyperuniversality conjecture φ=$\frac{1}{2}$. In addition, we have studied partially directed site lattice animals.