Analysis of experimental data within the statistical theory of critical phenomena

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) (14) decreases slower than the last two terms in (8) and therefore is really the most important after the leading term…”

“…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.…”

“…3 The terms written in (13) do not exhaust the singular ones in ) (r h c that lead to the divergent contributions into the isothermal compressibility of the "critical" fluid. Notable interest is the calculation of one more power term decreasing "faster" than those written in (13). Adding a term with exponent ' " n n  into the "critical" total PCF we can present its asymptotic form as follows:…”

“…, is long-range at the critical point, i.e. Having in mind expression (13) and taking into account the value (15) for the next to the leading exponent of the asymptotic decay of ) (r h c , we represent the simplest approximate expression for the function ) (r v c at 0 < r <  as follows:…”

“…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]).…”