  Knowledge of exact analytical functional forms for the pair correlation
function $g_2(r)$ and its corresponding structure factor $S(k)$ of disordered
many-particle systems is limited. For fundamental and practical reasons, it is
highly desirable to add to the existing data base of analytical functional
forms for such pair statistics. Here, we design a plethora of such pair
functions in direct and Fourier spaces across the first three Euclidean space
dimensions that are realizable by diverse many-particle systems with varying
degrees of correlated disorder across length scales, spanning a wide spectrum
of hyperuniform, typical nonhyperuniform and antihyperuniform ones. This is
accomplished by utilizing an efficient inverse algorithm that determines
equilibrium states with up to pair interactions at positive temperature that
precisely match targeted forms for both $g_2(r)$ and $S(k)$. Among other
results, we realize an example with the strongest hyperuniform property among
known positive-temperature equilibrium states, critical-point systems (implying
unusual 1D systems with phase transitions) that are not in the Ising
universality class, systems that attain self-similar pair statistics under
Fourier transformation, and an experimentally feasible polymer model. We show
that our pair functions enable one to achieve systems with a wide range of
translational order and self-diffusion coefficients $\cal D$, which are
inversely related to one another. One can design other realizable pair
statistics via linear combinations of our functions or by applying our inverse
procedure to other desirable functional forms. Our approach facilitates the
inverse design of materials with desirable physical and chemical properties by
tuning their pair statistics.
