2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/147802We analyze the critical line of $λϕ^4_4$ perturbatively in the bare coupling $λ_0$, by setting the daisy-improved renormalized mass to zero. By comparing to lattice data, we can then quantify the relation between the continuum cutoff and the lattice spacing; for the 4-dimensional hypercubic lattice we find $(Λa)_{C4} = 4.893$. We perform a similar analysis for $λϕ^6_3$, and find in 3 dimensions $(Λa)_{C3} = 4.67$. We present two theoretical predictions for $(Λa)$. For small $λ_0$, both the critical line and the renormalized mass near criticality are easily and accurately calculated from the lattice input parameters.6 pages, LaTeX, 4 figures using epsf.tex. Now auto-generates PSHigh Energy Physics - LatticeHigh Energy Physics - Phenomenologytext