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High orders in perturbation theory can be calculated by the Lipatov method.For most field theories, the Lipatov asymptotics has the functional form c a^N\Gamma(N+b) (N is the order of perturbation theory); relative corrections tothis asymptotics have the form of a power series in 1/N. The coefficients ofhigh order terms of this series can be calculated using a procedure analogousto the Lipatov approach and are determined by the second instanton in theconsidered field theory. These coefficients are calculated quantitatively forthe n-component \phi^4 theory under the assumption that the second instanton is(i) a combination of two elementary instantons and (ii) a sphericallyasymmetric localized function. The technique of two-instanton calculations isdeveloped, as well as the method for integrating over rotations of anasymmetric instanton in the coordinate state.Comment: 20 pages, PD

Higher order corrections to the Lipatov asymptotics in the ϕ4 theory