Triviality of $\phi^4_4$ theory: small volume expansion and new data

TL;DR

This paper investigates the triviality of four-dimensional phi^4 theory by combining numerical Monte Carlo simulations with a novel small volume expansion, providing evidence supporting the triviality scenario.

Contribution

It introduces a new small volume expansion approach and compares it with numerical data, offering insights into the triviality of phi^4_4 theory.

Findings

Numerical data near the continuum limit supports triviality.

The new expansion agrees with numerical results at small volumes.

Perturbation theory fails at small volumes, but the new expansion remains consistent.

Abstract

We study a renormalized coupling g and mass m in four dimensional phi^4 theory on tori with finite size z=mL. Precise numerical values close to the continuum limit are reported for z=1,2,4, based on Monte Carlo simulations performed in the equivalent all-order strong coupling reformulation. Ordinary renormalized perturbation theory is found to work marginally at z=2 and and to fail at z=1. By exactly integrating over the constant field mode we set up a renormalized expansion in z and compute three nontrivial orders. These results reasonably agree with the numerical data at small z. In the new expansion, the universal continuum limit exists as expected from multiplicative renormalizability. The triviality scenario is corroborated with significant precision.