Universal Crossover in Perturbation Theory with a Large Field Cutoff

TL;DR

This paper demonstrates that introducing a large field cutoff in lambda phi^4 models enhances perturbative series accuracy, with a universal function describing the transition between cutoff regimes, supported by numerical solutions for the anharmonic oscillator.

Contribution

It provides a numerical method to compute modified perturbative coefficients and reveals a universal crossover function for different cutoff regimes.

Findings

Large field cutoff improves perturbation series accuracy.

Universal function describes transition between cutoff regimes.

Approximate formulas extend well into low cutoff regions.

Abstract

For lambda phi^4 models, the introduction of a large field cutoff improves significantly the accuracy that can be reached with perturbative series but the calculation of the modified coefficients remains a challenging problem. We show that this problem can be solved numerically, and in the limits of large and small field cutoffs, for the ground state energy of the anharmonic oscillator. For the two lowest orders, the approximate formulas obtained in the large field cutoff limit extend unexpectedly far in the low field cutoff region. For the higher orders, the transition between the small field cutoff regime and the large field cutoff regime can be described in terms of a universal function.