English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We compute renormalization group fixed points and their spectrum in anultralocal approximation. We study a case of two competing non-trivial fixedpoints for a three-dimensional real $N$-component field: the O(N)-invariantfixed point vs.~the cubic-invariant fixed point. We compute the critical value$N_{c}$ of the cubic $\phi^{4}$-perturbation at the O(N)-fixed point. The O(N)fixed point is stable under a cubic $\phi^{4}$-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 valueof $N$ at the cubic invariant fixed point. Within the accuracy of ourcomputations, the two values coincide.Comment: 27 pages Latex2e, 4 figure

journal of statistical physics

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