Long-range correlations in the statistical theory of critical fluid

TL;DR

This paper develops a method to calculate detailed asymptotic behaviors of correlation functions in critical fluids, revealing new transcendental exponents and challenging the universality hypothesis near critical points.

Contribution

It introduces a consistent procedure for calculating non-classical asymptotic power terms in correlation functions, identifying new transcendental exponents and questioning the universality hypothesis.

Findings

Calculated new transcendental exponents 1.73494 and 2.26989.

Correlation functions closely match Lennard-Jones fluid data.

Results suggest universality hypothesis may not hold near critical points.

Abstract

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.