We report lattice simulations of $\phi_2^4$ and $O(N)\phi^4$ 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 $\phi^4$ continuum limit in two dimensions lead us to the result
g/μ 2 = 11.15 ± 0.06 stat ± 0.03 syst for the critical coupling. Furthermore we present preliminary
results for the three-dimensional $O(2)\phi^4$ model using the worm algorithm with the extention to
$O(N)\phi^4$ in D dimensions.