Minimally subtracted six loop renormalization of $O(n)$-symmetric ${\varphi }^4$ theory and critical exponents

Abstract

We present the perturbative renormalization group functions of $O(n)$-symmetric ${\varphi }^4$ theory in $4-2\epsilon$ dimensions to the sixth loop order in the minimal subtraction scheme. In addition, we estimate diagrams without subdivergences up to 11 loops and compare these results with the asymptotic behaviour of the beta function. Furthermore, we perform a resummation to obtain estimates for critical exponents in three and two dimensions.

comprehensive ancillary files provide details on the resummation of the critical exponents, the perturbative 6-loop expansions of critical exponents and RG functions, and epsilon expansions of 6-loop massless propagator integrals; v2: few misprints corrected and clarifications added

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