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Structural properties of self-attracting walks
A Ordemann1, E Tomer, G Berkolaiko
1Institut für Theoretische Physik III, Justus-Liebig-Universität Giessen, Heinrich-Buff-Ring 16, 35392 Giessen, Germany.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 3, 2001
Summary
Self-attracting walks exhibit a swelling-collapse transition, altering cluster structure. Below critical attraction, clusters resemble random walks; above, they become compact. At the transition, a new universality class emerges with fractal interfaces.
Area of Science:
- Statistical Physics
- Polymer Physics
- Complex Systems
Background:
- Self-attracting walks (SATW) model systems with attractive interactions.
- These systems exhibit a swelling-collapse transition analogous to polymer theta transitions.
- Understanding cluster structure below, at, and above this transition is crucial.
Purpose of the Study:
- To characterize the fractal dimensions of clusters and their interfaces for SATW.
- To identify the universality classes governing these structures.
- To analyze the behavior in one dimension where no transition occurs.
Main Methods:
- Scaling arguments
- Monte Carlo simulations
- Analytical derivations for 1D case
Main Results:
- Below critical attraction (u
- Above critical attraction (u>u(c)), clusters are compact (d(f)=d, d(I)=d-1).
- At the critical attraction (u=u(c)), a new universality class emerges with compact clusters but fractal interfaces (d(I)≈1.50 in d=2, d(I)≈2.73 in d=3).
- In 1D, analytical expressions for average visited sites and time were derived.
Conclusions:
- SATW exhibit distinct cluster structures and universality classes depending on the attractive interaction strength.
- The critical point signifies a transition to a novel state with fractal interfaces.
- The study provides a comprehensive characterization of SATW cluster properties across different dimensions and interaction regimes.