Some new exact critical-point amplitudes

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 ${\varphi }^4$ model in the limit $n\to \mathrm{\infty }$ as well as the quantum spherical model, with nearest-neighbor and long-range interactions (decreasing at long distances $r$ as $1\mathrm{/}{r}^{d+\sigma }$) is presented.