The Lattice Cutoff for $\lambda {\varphi }_4^4$ and $\lambda {\varphi }_3^6$

Abstract

We analyze the critical line of $\lambda {\varphi }_4^4$ perturbatively in the bare coupling ${\lambda }_0$, 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 $(\Lambda a{)}_{C4}=4.893$. We perform a similar analysis for $\lambda {\varphi }_3^6$, and find in 3 dimensions $(\Lambda a{)}_{C3}=4.67$. We present two theoretical predictions for $(\Lambda a)$. For small ${\lambda }_0$, both the critical line and the renormalized mass near criticality are easily and accurately calculated from the lattice input parameters.

Comments: 6 pages, LaTeX, 4 figures using epsf.tex. Now auto-generates PS