Quartic Anharmonicity in Different Spatial Dimensions

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.