Interacting linear polymers on three-dimensional Sierpinski fractals

Details Interacting linear polymers on three-dimensional Sierpinski fractals Interacting linear polymers on three-dimensional Sierpinski fractals

2002-05-24

arxiv.org/abs/cond-mat/0205509v1

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

Using self-avoiding walk model on three-dimensional Sierpinski fractals (3d SF) we have studied critical properties of self-interacting linear polymers in porous environment, via exact real-space renormalization group (RG) method. We have found that RG equations for 3d SF with base b=4 are much more complicated than for the previously studied b=2 and b=3 3d SFs. Numerical analysis of these equations shows that for all considered cases there are three fixed points, corresponding to the high-temperature extended polymer state, collapse transition, and the low-temperature state, which is compact or semi-compact, depending on the value of the fractal base b. We discuss the reasons for such different low--temperature behavior, as well as the possibility of establishing the RG equations beyond b=4.

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