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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Authors: | Pinn K Rehwald M Wieczerkowski Chr |
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Institution: | (1) Institut für Theoretische Physik I, Westfälische Wilhelms-Universität Münster, D-48149 Münster, Germany |
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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
4-perturbation at the O(N)-fixed point. The O(N)-fixed point is stable under a cubic
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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Keywords: | renormalization group fixed points cubic invariance |
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