Interacting linear polymers on three-dimensional Sierpinski fractals

TL;DR

This study investigates the critical behavior of self-interacting linear polymers on three-dimensional Sierpinski fractals using exact real-space renormalization group methods, revealing complex fixed points and temperature-dependent states.

Contribution

It provides the first detailed analysis of polymer critical properties on 3d Sierpinski fractals with base b=4, extending previous work on smaller bases.

Findings

Identification of three fixed points: extended, collapse, and low-temperature states.

Complexity increases in RG equations for b=4 compared to b=2 and b=3.

Low-temperature behavior varies with fractal base, showing compact or semi-compact states.

Abstract

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.