Two-loop corrections to large order behavior of φ4 theory

We consider the large order behavior of the perturbative expansion of the scalar φ4 field theory in terms of a perturbative expansion around an instanton solution. We have computed the series of the free energy up to two-loop order in two and three dimension. Topologically there is only an additiona...

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Published in:Nuclear physics. B 2017-09, Vol.922 (C), p.293-318
Main Authors: Malatesta, Enrico M., Parisi, Giorgio, Rizzo, Tommaso
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Parisi, Giorgio
Rizzo, Tommaso
description We consider the large order behavior of the perturbative expansion of the scalar φ4 field theory in terms of a perturbative expansion around an instanton solution. We have computed the series of the free energy up to two-loop order in two and three dimension. Topologically there is only an additional Feynman diagram with respect to the previously known one dimensional case, but a careful treatment of renormalization is needed. The propagator and Feynman diagrams were expressed in a form suitable for numerical evaluation. We then obtained explicit expressions summing over O(103) distinct eigenvalues determined numerically with the corresponding eigenfunctions.
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title Two-loop corrections to large order behavior of φ4 theory
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