  The scaling properties of the free energy and some of universal amplitudes of
a group of models belonging to the universality class of the quantum nonlinear
sigma model and the O(n) quantum $\phi^4$ model in the limit $n\to \infty$ as
well as the quantum spherical model, with nearest-neighbor and long-range
interactions (decreasing at long distances $r$ as $1/r^{d+\sigma}$) is
presented.
