Resummation of the Two Distinct Large Logarithms in the Broken $O(N)$-symmetric $ϕ^4$-model

C. Wiesendanger

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arXiv · hep-th/9609129

Resummation of the Two Distinct Large Logarithms in the Broken $O(N)$-symmetric $ϕ^4$-model

C. Wiesendanger

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Abstract

The loop-expansion of the effective potential in the $O(N)$-symmetric $ϕ^4$-model contains generically two types of large logarithms. To resum those systematically a new minimal two-scale subtraction scheme $\tMS$ is introduced in an $O(N)$-invariant generalization of $\MS$. As the $\tMS$ beta functions depend on the renormalization scale-ratio a large logarithms resummation is performed on them. Two partial $\tMS$ renormalization group equations are derived to turn the beta functions into $\tMS$ running parameters. With the use of standard perturbative boundary conditions, which become applicable in $\tMS$, the leading logarithmic $\tMS$ effective potential is computed. The calculation indicates that there is no stable vacuum in the broken phase of the theory for $1<N\leq 4$.

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C. Wiesendanger. 1996-09-16. Resummation of the Two Distinct Large Logarithms in the Broken $O(N)$-symmetric $ϕ^4$-model. https://arxiv.org/abs/hep-th/9609129

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