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

Details Triviality of $φ^4_4$ theory: small volume expansion and new data Triviality of $φ^4_4$ theory: small volume expansion and new data

2010-12-02

arxiv.org/abs/1012.0404v1

Nucl.Phys.B846:316-337,2011

Physics

High Energy Physics

High Energy Physics - Lattice

27 pages, 7 figures, 4 tables

Scientific paper

10.1016/j.nuclphysb.2011.01.006

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.

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