Temperature-dependent structural behavior of self-avoiding walks on Sierpinski carpets

We study the temperature-dependent structural behavior of self-avoiding walks (SAWs) on two-dimensional Sierpinski carpets as a simple model of polymers adsorbed on a disordered surface. Thereby, the Sierpinski carpet defines two types of sites with energy 0 and >0, respectively, yielding a deterministic fractal energy landscape. In the limiting cases of temperature T→0 and T→, the known behaviors of SAWs on Sierpinski carpets and on regular square lattices, respectively, are recovered. For finite temperatures, the structural behavior is found to be intermediate between the two limiting cases; the characteristic exponents, however, display a nontrivial dependence on temperature. © 2007 The American Physical Society.