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Directed polymers in random media under confining force.

Hyeong-Chai Jeong¹

¹Department of Physics and Institute for Fundamental Physics, Sejong University, Seoul 143-747, Korea. hcj@sejong.ac.kr

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|October 26, 2005

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We studied directed polymers in random potentials. The polymer

Area of Science:

Statistical physics
Polymer physics
Condensed matter theory

Background:

Directed polymers in random media are fundamental models in statistical physics.
Understanding their scaling behavior under external forces is crucial for various applications.
Confining forces introduce additional complexity to polymer behavior.

Purpose of the Study:

To investigate the scaling behavior of a directed polymer in a 2D random potential under a confining force.
To determine the relationship between polymer length and its radius of gyration and energy fluctuation.
To introduce and validate a numerical method for finding the polymer's ground state.

Main Methods:

Utilized an energy argument to derive scaling relations.
Developed an algorithm for finding the exact ground state of the polymer.

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Employed numerical simulations to confirm theoretical conjectures.

Main Results:

Conjectured scaling relations for the radius of gyration (Rg(N) ~ N^nu) and energy fluctuation (deltaE(N) ~ N^omega).
Derived specific exponents nu = 1/(1+alpha) and omega = (1+2alpha)/(4+4alpha) for alpha >= 1/2.
Confirmed the conjectures numerically using the developed algorithm.

Conclusions:

The study provides theoretical and numerical evidence for the scaling behavior of confined directed polymers.
The developed algorithm offers an efficient way to study ground states in such systems.
Results contribute to the understanding of polymer physics in disordered environments.