Bogolyubov Kyiv Conference "Problems of Theoretical and Mathematical Physics"

Whether the Hypothesis of Conformal Invariance Is Fulfilled Near the Critical Points of Fluids?

22 Sep 2026, 13:20

20m

Conference Hall (Bogolyubov Institute for Theoretical Physics)

Oral STATISTICAL PHYSICS AND SOFT MATTER

Speaker

Prof. A.V. Chalyi (Bogomolets National Medical University)

Description

L.A. Bulavin$^{1,2}$, E.G. Rudnikov$^{1,3}$, K.O. Cherevko$^{1,2}$, A.V. Chalyi$^4$

1 Department of Molecular Physics, Faculty of Physics, Kyiv National Taras Shevchenko University, Volodymyrska Str., 64 Kyiv 01601, Ukraine
2 Institute for Safety Problems of Nuclear Power Plants of the NAS of Ukraine, Lysohirska Street, 12, Kyiv 03028, Ukraine
3 Department of Biomedical Cybernetics, Faculty of Biomedical Engineering, National Technical University of Ukraine "Ihor Sikorsky Kyiv Polytechnic Institute", Beresteyskiy Ave., 37 Kyiv 03056, Ukraine
4 Department of Medical and Biological Physics and Informatics, Bogomolets National Medical University, Shevchenko Blvd., 13, Kyiv 01601, Ukraine

Conformal transformations were introduced in the physics of phase transitions by A.M. Polyakov [1]. Based on the hypothesis of conformal invariance (CI), scale invariance with anomalous dimensions was proposed [2], both in the theory of critical phenomena for fluctuating quantities and in hadronic interactions. The CI hypothesis also proves to be fundamental in interdisciplinary research, for example, to explain the formation of hexagonal structures in the system of grid cells in the brain (2014 Nobel Prize in Physiology and medicine) [3] An important consequence of CI hypothesis in the physics of phase transitions, according to [4], is the orthogonality relation for two fluctuating quantities of transitions with different scale dimensions within the algebra of fluctuating quantities, which was proposed by V.L. Pokrovskii [5] (see also [6]). The aim of this work is to verify for the first time the CI hypothesis for the liquid-vapor critical points of single-component fluids based on existing experimental data. For this purpose, we used experimental data for carbon dioxide [7], water [8,9], and polyol ester (POE9) lubricant with a higher critical temperature, for which experimental data are available in the scientific literature [10]. These fluids have critical temperatures $T_C=304.1$K, $T_C=647.1$ K and $T_C=970.0$ K and critical densities $\rho_C=467.6$ kg/m3, $\rho_C=322.0$ kg/m3 and $\rho_C=220.3$ kg/m3, respectively. It was proven that for the studied fluids the hypothesis of conformal invariance holds in temperature intervals determined from experimental data near their liquid-vapor critical points. The values of the temperature intervals in which the hypothesis of conformal invariance near the liquid-vapor critical points is fulfilled depend on the absolute values of the critical parameters of the studied fluids. Confirmation of the CI hypothesis also means that the temperature derivative of the coexistence-curve diameter retains the weak singularity with the exponent of the isochoric heat capacity [11-13].

1. A.M. Polyakov, Conformal symmetry of critical fluctuations, JETP Lett. 12, 381–383 (1970).
2. A.A. Migdal, Conformal invariance and bootstrap, Phys. Lett. B 37(4), 386–388 (1971). doi: 10.1016/0370-2693(71)90211-5
3. A.V. Chalyi. What is Medicine? Basic Principles of Physics in Medicine and Beyond, Springer Nature Switzerland AG (2024). https//doi.org/10/1007/978-3031-64979-0
4. L.P. Kadanoff, Operator algebra and the determination of critical indices, Phys. Rev. Lett. 23(25), 1430–1433 (1969).
5. V.L. Pokrovskii, Feasibility of experimental verification of the conformal invariance hypothesis, JETP Lett. 17, 219–221 (1973).
6. A.Z. Patashinsky, V.L. Pokrovsky, Fluctuation Theory of Phase Transitions (Pergamon Press, Oxford, 1979).
7. R. Span, W. Wagner, Equations of state for technical applications. III. Results for polar fluids, Int. J. Thermophys. 24(1), 111–162(2003). doi: 10.1023/A:1022362231796
8. M.Z. Southard, D.W. Green, Perry’s Chemical Engineers’ Handbook, 9th ed. (McGraw-Hill Education, New York, 2019).
9. REFPROP Database, National Institute of Standards and Technology, SRD 23, Version 10 (2018). doi: 10.18434/T4/1502528
10. T.J. Bruno, T.J. Fortin, M.L. Huber, A. Laesecke, E.W. Lemmon, E. Mansfield, M.O. McLinden, S.L. Outcalt, R.A. Perkins, K.N.Urness, J.A. Widegren, Thermophysical Properties of Polyol Ester Lubricants, NISTIR 8263 (National Institute of Standards and Technology, 2019). doi: 10.6028/NIST.IR.8263
11. L.M. Artyukhovskaya, E.T. Shmanskaya, Yu.I. Shimanskii, Heptane coexistence curve near the critical point. JETP 63(3), 2153-2164, (1972).
12. L.A. Bulavin, Yu.I. Shimanskii. The singularity of the coexistence-curve diameter of ethane. JETP Lett 29(8) 482 (1979).
13. A.V. Chalyi, L.A. Bulavin, K.A. Chalyy. On the neutron optics of liquids, J/ Mol. Liquids 383, 121979 (2023).,