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Fixing the fixed-point system—Applying Dynamic Renormalization Group to systems with long-range interactions

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  • Katzav, Eytan

Abstract

In this paper, a mode of using the Dynamic Renormalization Group (DRG) method is suggested in order to cope with inconsistent results obtained when applying it to a continuous family of one-dimensional nonlocal models. The key observation is that the correct fixed-point dynamical system has to be identified during the analysis in order to account for all the relevant terms that are generated under renormalization. This is well established for static problems, however poorly implemented in dynamical ones. An application of this approach to a nonlocal extension of the Kardar–Parisi–Zhang equation resolves certain problems in one-dimension. Namely, obviously problematic predictions are eliminated and the existing exact analytic results are recovered.

Suggested Citation

  • Katzav, Eytan, 2013. "Fixing the fixed-point system—Applying Dynamic Renormalization Group to systems with long-range interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(8), pages 1750-1755.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:8:p:1750-1755
    DOI: 10.1016/j.physa.2013.01.010
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    References listed on IDEAS

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    1. Katzav, Eytan, 2002. "Exact result vs. dynamic renormalization group analysis for the nonlocal molecular-beam-epitaxy equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 308(1), pages 25-28.
    2. Katzav, Eytan, 2002. "Exact result vs. dynamic renormalization group analysis for the non-local Kardar–Parisi–Zhang equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 309(1), pages 79-84.
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    Cited by:

    1. Hu, Xiongpeng & Hao, Dapeng & Xia, Hui, 2023. "Improved finite-difference and pseudospectral schemes for the Kardar–Parisi–Zhang equation with long-range temporal correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 619(C).

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