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I.M.Suslov (P.L.Kapitza Institute for Physical Problems)
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Renormalization group functions of \phi^4 theory in the strong coupling limit: analytical results.
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Attempts of reconstruction of the \beta-function for
\phi^4 theory, made previously by summation of perturbation
series, lead to asymptotics \beta(g)=\beta_\infty g^\alpha
for g\to\infty, where \alpha\approx 1 for space dimensions
d=2,3,4. The natural hypothesis arises, that \beta(g) \sim g
for large g at all d. Consideration of zero-dimensional case
confirms this hypothesis and and reveals the mechanism of its
origin: it is related with zeroing of one of functional integrals.
It makes possble to generalize considerations to arbitrary
d-dimensional case and confirm linear asymptotics for
\beta-function at all d. Asymptotical behavior for
anomalous dimensions is shown to be constant.