Monte Carlo simulation of ${\varphi }_2^4$ and $O(N){\varphi }_3^4$ theories

We report lattice simulations of ${\varphi }_2^4$ and $O(N){\varphi }^4$ models, performed by means of a Monte Carlo method based on the all-order strong coupling expansion (worm algorithm). The investigation of the non-perturbative features of the ${\varphi }^4$ continuum limit in two dimensions lead us to the result $g\mathrm{/}{\mu }^2=11.15\pm {0.06}_{stat}\pm {0.03}_{syst}$ for the critical coupling. Furthermore we present preliminary results for the three-dimensional $O(2){\varphi }^4$ model using the worm algorithm with the extention to $O(N){\varphi }^4$ in $D$ dimensions.