Scaling laws and triviality bounds in the lattice φ4 theory

Abstract

The lattice φ4 theory in four space-time dimensions is most likely "trivial", i.e. its continuum limit is a free field theory. However, for small but positive lattice spacing a at energies well below the cutoff mass Λ = 1/a, the theory effectively behaves like a continuum theory with particle interactions, which may be appreciable. By a combination of known analytical methods, we here determine the maximal value of the renormalized coupling at zero momentum as a function of Λ/m, where m denotes the mass of the scalar particle in the theory. Moreover, a complete solution of the model is obtained in the sense that all low energy amplitudes can be computed with reasonable estimated accuracy for arbitrarily chosen bare coupling and mass in the symmetric phase region.