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On the Stability of the O(N)-Invariant and the Cubic-Invariant 3-Dimensional $N$-Component Renormalization Group Fixed Points in the Hierarchical Approximation

K. Pinn·M. Rehwald·C. Wieczerkowski
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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 non-trivial 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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K. Pinn, M. Rehwald, C. Wieczerkowski. 1998-05-15. On the Stability of the O(N)-Invariant and the Cubic-Invariant 3-Dimensional $N$-Component Renormalization Group Fixed Points in the Hierarchical Approximation. https://doi.org/10.1023/a%3A1004568925547

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