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Zero-temperature directed polymer in random potential in 4+1 dimensions.

Jin Min Kim1

  • 1Department of Physics and Research Institute for the Origin of Matter and the Evolution of Galaxies, Soongsil University, Seoul 156-743, Korea.

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|January 14, 2017
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Summary
This summary is machine-generated.

This study investigates directed polymers in random potentials, finding key scaling exponents for energy fluctuations and polymer length. Results suggest the upper critical dimension for the Kardar-Parisi-Zhang equation exceeds 4+1 dimensions.

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Area of Science:

  • Statistical physics
  • Condensed matter physics
  • Polymer physics

Background:

  • Directed polymers in random potentials are fundamental models in statistical physics.
  • Understanding their low-temperature behavior is crucial for various physical phenomena.

Purpose of the Study:

  • To characterize the scaling behavior of a directed polymer in a 4+1 dimensional random potential at zero temperature.
  • To determine the dynamic exponent and saturation exponents governing polymer properties.

Main Methods:

  • Numerical simulations of a directed polymer model.
  • Analysis of energy fluctuations and end-to-end distance as a function of polymer length and system size.
  • Calculation of scaling exponents using established relationships.

Main Results:

  • Energy fluctuation ΔE(t) scales with polymer length t as t^{β} with β=0.159±0.007.
  • At saturation, ΔE(L) scales with system size L as L^{α} with α=0.275±0.009.
  • The dynamic exponent z≈1.73 was obtained, satisfying the scaling relation α+z=2.

Conclusions:

  • The study provides precise estimates for critical exponents governing directed polymer behavior in 4+1 dimensions.
  • The findings indicate that the upper critical dimension of the Kardar-Parisi-Zhang equation is greater than 4+1 dimensions.