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On the Stability of the O(N)-Invariant and the Cubic-Invariant Three-Dimensional N-Component Renormalization-Group Fixed Points in the Hierarchical Approximation

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Abstract

We compute renormalization-group fixed points and their spectrum in an ultralocal approximation. We study a case of two competing nontrivial fixed points for a three-dimensional real N-component field: the O(N)-invariant fixed point vs. the cubic-invariant fixed point. We compute the critical value N c of the cubic φ 4-perturbation at the O(N)-fixed point. The O(N)-fixed point is stable under a cubic φ 4-perturbation below N c; above N c it is unstable. The Critical value comes out as 2.219435<N c<2.219436 in the ultralocal approximation. We also compute the critical value of N at the cubic invariant fixed point. Within the accuracy of our computations, the two values coincide.

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Authors and Affiliations

  1. Institut für Theoretische Physik I, Westfälische Wilhelms-Universität Münster, D-48149, Münster, Germany

    K. Pinn, M. Rehwald & Chr. Wieczerkowski

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  1. K. Pinn
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  2. M. Rehwald
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  3. Chr. Wieczerkowski
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Pinn, K., Rehwald, M. & Wieczerkowski, C. On the Stability of the O(N)-Invariant and the Cubic-Invariant Three-Dimensional N-Component Renormalization-Group Fixed Points in the Hierarchical Approximation. Journal of Statistical Physics 95, 1–22 (1999). https://doi.org/10.1023/A:1004568925547

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