Scaling behavior of linear polymers in disordered media

Area of Science:

• Polymer Physics
• Statistical Mechanics
• Condensed Matter Physics

Background:

• Universal scaling properties of linear polymers in disordered media are often modeled using self-avoiding walks (SAWs) on percolation clusters.
• The critical exponent nu(SAW) describes these scaling properties, typically determined via static averaging methods in simulations.
• Static averaging implicitly assumes an 'average' SAW, which may not capture asymptotic scaling behavior.

Purpose of the Study:

• To challenge the conventional use of static averaging for determining SAW properties.
• To assert that only kinetic averaging can accurately capture asymptotic scaling behavior.
• To develop and apply a theoretical framework for calculating SAW scaling exponents using kinetic averaging.

Main Methods:

• Heuristic arguments to support the kinetic averaging hypothesis.
• Development of a renormalizable field theory for SAW statistics.
• Two-loop order calculations within the field theory framework.

Main Results:

• Demonstration that kinetic averaging is essential for asymptotic scaling.
• Calculation of the critical exponent nu(SAW) using the new theoretical approach.
• Determination of the exponent nu(max) for the longest SAW and a family of multifractal exponents nu(alpha).

Conclusions:

• Kinetic averaging provides a more accurate description of polymer scaling on percolation clusters than static averaging.
• The developed field theory and calculation methods offer a robust tool for analyzing SAW properties.
• The findings have implications for understanding polymer behavior in complex environments.