  Using the approach formulated in the previous papers of the author, a
consistent procedure is developed for calculating non-classical asymptotic
power terms in the total and the direct correlation functions of a critical
fluid. Analyzing the Ornstein-Zernike equation allows us to find, for the first
time, the values of transcendental exponents 1.73494 and 2.26989 which
determine the asymptotic terms next to the leading one in the total correlation
function. It is shown that already the simplest approximation based on only two
asymptotic terms leads to the correlation functions, which are quantitatively
close to the corresponding ones of the Lennard-Jones fluid (argon) in the
near-critical state. The obtained results open a way for consistent theoretical
interpretation of the experimental data on the critical characteristics of real
substances. Both the theoretical arguments and analysis of published data on
the experimentally measured critical exponents of real fluids lead to the
conclusion that the known assumption of the sameness of the critical
characteristics of the Ising model and the fluid in the vicinity of critical
point (the universality hypothesis) should be questioned.
