  We study correlation functions of the Calogero-Sutherland model in the whole
range of the interaction parameter. Using the replica method we obtain
analytical expressions for the long-distance asymptotics of the one-body
density matrix in addition to the previously derived asymptotics of the
pair-distribution function [D.M. Gangardt and A. Kamenev, Nucl. Phys. B, 610,
578 (2001)]. The leading analytic and non-analytic terms in the short-distance
expansion of the one-body density matrix are discussed. Exact numerical results
for these correlation functions are obtained using Monte Carlo techniques for
all distances. The momentum distribution and static structure factor are
calculated. The potential and kinetic energies are obtained using the
Hellmann-Feynman theorem. Perfect agreement is found between the analytical
expressions and numerical data. These results allow for the description of
physical regimes of the Calogero-Sutherland model. The zero temperature phase
diagram is found to be of a crossover type and includes quasi-condensation,
quasi-crystallization and quasi-supersolid regimes.
