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

Understand

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.