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

نویسندگان

  • K. Pinn
  • M. Rehwald
چکیده

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 Nc of the cubic φ -perturbation at the O(N)-fixed point. The O(N) fixed point is stable under a cubic φ-perturbation belowNc, above Nc it is unstable. The critical value comes out as 2.219435 < Nc < 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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تاریخ انتشار 1999