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Perfect Lattice Perturbation Theory: A Study Of The Anharmonic Oscillator

Author

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  • W. BIETENHOLZ

    (HLRZ c/o Forschungszentrum Jülich, D-52425 Jülich, Germany;
    NORDITA, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark)

  • T. STRUCKMANN

    (Physics Department University of Wuppertal D-42097 Wuppertal, Germany)

Abstract

As an application of perfect lattice perturbation theory, we construct anO(λ)perfect lattice action for the anharmonic oscillator analytically in momentum space. In coordinate space, we obtain a set of 2-spin and 4-spin couplings∝λ, which we evaluate for various masses. These couplings never involve variables separated by more than two lattice spacings. TheO(λ)perfect action is simulated and compared to the standard action. We discuss the improvement for the first two energy gapsΔE1,ΔE2and for the scaling quantityΔE2/ΔE1in different regimes of the interaction parameter, and of the correlation length. For the quartic oscillator — which corresponds to an asymptotically free theory — we also discuss a classically perfect action. The single gaps perform very well, which corresponds to a clearly improved asymptotic scaling. On the other hand, it turns out to be difficult to demonstrate an improvement for the scaling ratio.

Suggested Citation

  • W. Bietenholz & T. Struckmann, 1999. "Perfect Lattice Perturbation Theory: A Study Of The Anharmonic Oscillator," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 10(04), pages 531-553.
    • Handle: RePEc:wsi:ijmpcx:v:10:y:1999:i:04:n:s0129183199000413
    DOI: 10.1142/S0129183199000413
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