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Using the approach formulated in the previous papers of the author, aconsistent procedure is developed for calculating non-classical asymptoticpower terms in the total and the direct correlation functions of a criticalfluid. Analyzing the Ornstein-Zernike equation allows us to find, for the firsttime, the values of transcendental exponents 1.73494 and 2.26989 whichdetermine the asymptotic terms next to the leading one in the total correlationfunction. It is shown that already the simplest approximation based on only twoasymptotic terms leads to the correlation functions, which are quantitativelyclose to the corresponding ones of the Lennard-Jones fluid (argon) in thenear-critical state. The obtained results open a way for consistent theoreticalinterpretation of the experimental data on the critical characteristics of realsubstances. Both the theoretical arguments and analysis of published data onthe experimentally measured critical exponents of real fluids lead to theconclusion that the known assumption of the sameness of the criticalcharacteristics of the Ising model and the fluid in the vicinity of criticalpoint (the universality hypothesis) should be questioned.

Long-range correlations in the statistical theory of critical fluid