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 correlation function h c ( r ) of a “critical” fluid. Analyzing the Ornstein-Zernike equation with taking account of the contribution ˜ h c 4 ( r ) in the direct correlation function c c ( r ) allows us to find, for the first time, the values of transcendental exponents n ′ = 1.73494... and n ″ = 2.26989... which determine the asymptotic terms next to the leading one in h c ( r ) . It is shown that already the simplest approximation based on only two asymptotic terms, ˜ r − 6 / 5 (it was found earlier) and ˜ r − n ′ , leads to the functions h c ( r ) and c c ( r ) , which agree (at least, qualitatively) with the corresponding correlation functions 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 similarity of the critical characteristics of the Ising model and the fluid in the vicinity of critical point (the “universality hypothesis”) should be questioned.

中文翻译：

---

流体临界统计理论中的长程相关性

摘要 使用作者之前论文中制定的方法，开发了一种一致的程序，用于计算“临界”流体的总相关函数 hc ( r ) 中的非经典渐近幂项。分析 Ornstein-Zernike 方程并考虑直接相关函数 cc ( r ) 中的贡献 ~ hc 4 ( r ) 使我们能够首次找到超越指数的值 n ' = 1.73494...和n ″ = 2.26989... 确定 hc ( r ) 中前导项旁边的渐近项。结果表明，仅基于两个渐近项 ˜ r − 6 / 5（较早发现）和 ˜ r − n ′ 的最简单近似导致函数 hc ( r ) 和 cc ( r ) 一致（至少，定性）与处于近临界状态的 Lennard-Jones 流体（氩）的相应相关函数。获得的结果为对真实物质临界特性的实验数据进行一致的理论解释开辟了道路。对实际流体的实验测量临界指数的已发表数据的理论论证和分析得出的结论是，Ising 模型的临界特性与临界点附近的流体的相似性的已知假设（“普遍性”）。假设”）应该受到质疑。