Nonclassical critical indices in the statistical theory of liquids and equations of state with regular and scaling components

Long-range correlations in the statistical theory of fluid criticality

“…Thus, in the framework of the theory [10,11] we succeeded in finding the numerical value of the exponent ' n , determining the asymptotic behavior of the next to the leading term in the singular part of the "critical" PCF (13). The found exponent (15) in (14) decreases slower than the last two terms in (8) and therefore is really the most important after the leading term 5 / 24 ~ r…”

“…Using these results, as well as exact conditions on the "critical" PCFs, in Section 3 we find self-consistent expressions for these PCFs and demonstrate the possibility of applying them to interpreting (even at a quantitative level) experimental data for real fluid (argon) near the critical point. Further (Section 4), we argue that the approach developed in this paper (and in [10,11,[13][14][15]) allows us to describe experimental data on the critical features of the thermodynamic functions of real fluids more accurately than the 3D Ising model. This means that the mentioned "universality hypothesis", which relates the "critical" fluid and the lattice gas (the Ising model) to one and the same universality class, hardly takes place.…”

“…with the asymptotic behavior (14) and then let us study the difference A . Then, in analogy with the derivation of (A4), we obtain from (A8): (A9)…”

“…It is important to note that if ' n <12/5, the asymptotic term ' 5 / 18 ~n r   in (14) decreases more slowly than the last two terms in the expression (8). Therefore, below we will find the exponent ' n in the range…”

“…Besides, the approach [10] was applied in [11] to the calculation of the next to the leading terms in the expressions for the correlation lengths (the socalled "correction-to-scaling" terms, following the terminology of [12]). Good quantitative agreement of the theory [10,11] and experiment opened a way to accurate processing of the experimental data on the critical properties of real substances (see [13][14][15]).…”