A study of large field configurations in MC simulations

TL;DR

This paper introduces a novel perturbative approach in scalar field theory that neglects large field configurations, improving convergence of series and outperforming traditional methods in certain regimes, supported by Monte Carlo simulations.

Contribution

The paper presents a new method for handling large field configurations in scalar field theories, enhancing perturbative series convergence and applicability to non-Borel summable series.

Findings

Modified series converge exponentially close to exact values

Method outperforms Pade and Borel summation for large coupling

Monte Carlo simulations support the dilution hypothesis of large fields

Abstract

We discuss a new approach of scalar field theory where the small field contributions are treated perturbatively and the large field configurations (which are responsible for the asymptotic behavior of the perturbative series) are neglected. In two Borel summable lambda phi ^4 problems improved perturbative series can be obtained by this procedure. The modified series converge towards values exponentially close to the exact ones. For lambda larger than some critical value, the method outperforms Pade approximants and Borel summations. The method can also be used for series which are not Borel summable such as the double-well potential series and provide a perturbative approach of the instanton contribution. Semi-classical methods can be used to calculate the modified Feynman rules, estimate the error and optimize the field cutoff. We discuss Monte Carlo simulations in one and two dimensions which support the hypothesis of dilution of large field configurations used in these semi-classical calculations. We show that Monte Carlo methods can be used to calculate the modified perturbative series.