  A path-integral method effective beyond the perturbation expansion approach
is suggested to consider the quartic anharmonicity in different spatial
dimensions. Due to an optimal representation of the partition function, the
leading term has already taken into account the correct strong-coupling
behaviour. In the simplest cases of zero and one dimension we have obtained
reasonable results in a simple way. Then, this technique is applied to the
superrenormalizable scalar theory phi^4_2 in two dimensions. This results in an
accurate estimation of the ground-state energy that provides exact weak- and
strong-coupling behaviour already in the leading-order approximation. The
next-to-leading terms give rise in insignificant corrections.
