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The standard lattice perturbation theory leads to the asymptotic seriesbecause of the incorrect interchange of the summation and integration. However,changing the initial approximation of the perturbation theory, one can generatethe convergent series. We study the lattice $\phi^4$-model and compare theoperator $\langle\phi_n^2\rangle$ calculated using the convergent series andobtained by Monte Carlo simulations.

Convergent Perturbation Theory for the lattice $\phi^4$-model