Triviality of ${\varphi }_4^4$ theory: small volume expansion and new data

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.

arXiv comment27 pages, 7 figures, 4 tables

References in corpus (3)

• The Schrödinger Functional - a Renormalizable Probe for Non-Abelian Gauge Theories
• Two Loop Computation of the Schroedinger Functional in Lattice QCD
• Precision check on triviality of phi^4 theory by a new simulation method

Cited by in corpus (21)

• Approaches to the sign problem in lattice field theory
• Lattice study of the Silver Blaze phenomenon for a charged scalar phi-4 field
• Monte Carlo simulation of the SU(3) spin model with chemical potential in a flux representation
• Surface worm algorithm for abelian Gauge-Higgs systems on the lattice
• Dual lattice simulation of the U(1) gauge-Higgs model at finite density - an exploratory proof-of-concept study
• Worm algorithms for the 3-state Potts model with magnetic field and chemical potential
• Quantum sensors for the generating functional of interacting quantum field theories
• Gauge and matter fields as surfaces and loops - an exploratory lattice study of the Z(3) Gauge-Higgs model
• Triviality of ${\phi }^4$ theory in a finite volume scheme adapted to the broken phase
• Spectroscopy in finite density lattice field theory: An exploratory study in the relativistic Bose gas
• Finite size scaling and triviality of ϕ^4 theory on an antiperiodic torus
• Investigation of New Methods for Numerical Stochastic Perturbation Theory in ${\phi }^4$ Theory
• Triviality problem and the high-temperature expansions of the higher susceptibilities for the Ising and the scalar field models on four-, five- and six-dimensional lattices
• Finite-size scaling for four-dimensional Higgs-Yukawa model near the Gaussian fixed point
• Remarks on the construction of worm algorithms for lattice field theories in worldline representation
• Finite density condensation and scattering data - a study in ${\varphi }^4$ lattice field theory
• New techniques and results for worldline simulations of lattice field theories
• Exploring Higgs boson Yukawa interactions with a scalar singlet using Dyson-Schwinger equations
• Dynamical Mass Generation in Wick Cutkosky Model
• Two Higgs Doublet Model with Scalar Mediation via Yukawa Interactions
• Studies of Wick Cutkosky model in light of its classical ground state using Dyson Schwinger equations