A. Yu. Zakharov, I. K. Loktionov, “Classical statistics of one-component systems with model potentials”, TMF, 119:1 (1999), 167–176; Theoret. and Math. Phys., 119:1 (1999), 532

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Teoreticheskaya i Matematicheskaya Fizika, 1999, Volume 119, Number 1, Pages 167–176
DOI: https://doi.org/10.4213/tmf735 (Mi tmf735)

This article is cited in 21 scientific papers (total in 21 papers)

Classical statistics of one-component systems with model potentials

A. Yu. Zakharov^a, I. K. Loktionov^b

^a Novgorod State University after Yaroslav the Wise
^b Donetsk National Technical University

Full-text PDF (200 kB) Citations (21)

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DOI: https://doi.org/10.4213/tmf735

Abstract: We obtain a functional integral representation of the configuration integral for one-component classical systems with two-particle potentials admitting the Fourier expansion. In this representation, the integrand is factored with respect to the atomic coordinates. The “monoatomic” factors are universal (i.e., independent of the explicit form of the interatomic potential). We obtain a sufficient condition for spontaneous symmetry breaking in continuous classical statistics models. We investigate the case of model potentials with a nonnegative Fourier transform. The functional integral for this class of potentials is calculated using the saddle-point method. We prove the existence of phase transitions for some model potentials.

Received: 26.03.1998
Revised: 03.09.1998

English version:
Theoretical and Mathematical Physics, 1999, Volume 119, Issue 1, Pages 532–539
DOI: https://doi.org/10.1007/BF02557350

Bibliographic databases:

Language: Russian

Citation: A. Yu. Zakharov, I. K. Loktionov, “Classical statistics of one-component systems with model potentials”, TMF, 119:1 (1999), 167–176; Theoret. and Math. Phys., 119:1 (1999), 532–539

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf735

https://doi.org/10.4213/tmf735

https://www.mathnet.ru/eng/tmf/v119/i1/p167

This publication is cited in the following 21 articles:

V. B. Bobrov, “On the closed interpolation equation of state for a simple liquid”, High Temperature, 61:3 (2023), 320–327
I. K. Loktionov, “Equation of state for a liquid with double exponential potential”, High Temperature, 59:2 (2021), 148–155
Brilliantov V N. Rubi J.M. Budkov Yu.A., “Molecular Fields and Statistical Field Theory of Fluids: Application to Interface Phenomena”, Phys. Rev. E, 101:4 (2020), 042135
Budkov Yu.A., “Statistical Field Theory of Ion-Molecular Solutions”, Phys. Chem. Chem. Phys., 22:26 (2020), 14756–14772
Budkov Yu.A., “Statistical Theory of Fluids With a Complex Electric Structure: Application to Solutions of Soft-Core Dipolar Particles”, Fluid Phase Equilib., 490 (2019), 133–140
I. K. Loktionov, “Mathematical modeling of thermodynamic properties of a fluid based on the Yukawa double potential: Analytical results”, High Temperature, 57:5 (2019), 648–654
Zakharov A.Yu. Schneider A.A. Zavorotnev Yu.D. Metlov L.S., International Scientific and Practical Conference on Innovations in Engineering and Technology, IOP Conference Series-Materials Science and Engineering, 441, ed. Sapozhkov S., IOP Publishing Ltd, 2018
I. K. Loktionov, “Prediction of equilibrium thermodynamic properties of simple liquids in the model with four-parametric oscillating interaction potential”, Tech. Phys., 60:3 (2015), 317
I. K. Loktionov, “Studying Equilibrium Thermophysical Properties of Simple Liquids Based on a Four-Parameter Oscillating Interaction Potential”, High Temperature, 52:3 (2014), 391–403
I. K. Loktionov, “Application of two-parameter oscillating interaction potentials for specifying the thermophysical properties of simple liquids”, High Temperature, 50:6 (2012), 708–716
I. K. Loktionov, “Studying the temperature dependences of thermodynamic properties of cesium vapors using the three-parameter model pair interaction potential”, High Temperature, 50:3 (2012), 359–365
Loktionov I.K., “Teplofizicheskie svoistva sistem s chetyrekhparametricheskim ostsilliruyuschim potentsialom vzaimodeistviya”, Ultrazvuk i termodinamicheskie svoistva veschestva, 2012, no. 38, 49–53
Zakharov A.Yu., “Metod funktsionalnogo integrirovaniya v kontinualnoi modeli binarnykh rastvorov. svobodnaya energiya i izbytochnaya entropiya”, Vestnik novgorodskogo gosudarstvennogo universiteta im. yaroslava mudrogo, 2012, no. 3, 8–12
I. K. Loktionov, “Thermodynamic Properties of One-Component Systems with Pair Two-Parameter Interaction Potentials”, High Temperature, 49:4 (2011), 512–519
Zakharov, AY, “Ensembles in classical statistical mechanics and their unification via nonlinear field theory”, International Journal of Quantum Chemistry, 100:4 (2004), 442
Zakharov, AY, “Intermolecular forces and random fields: Mutual renormalizations in classical statistical mechanics”, International Journal of Quantum Chemistry, 96:3 (2004), 234
Zakharov, AY, “Quasi-particles, random fields, and phase transitions in classical statistical mechanics”, Russian Journal of Physical Chemistry, 77 (2003), S1
Zakharov, AY, “The concept of elementary excitations in classical statistical mechanics”, Technical Physics Letters, 27:7 (2001), 560
Loktionov, IK, “One-dimensional classical model with phase transition”, High Temperature, 39:2 (2001), 325
Loktionov, IK, “Determination of the critical parameters of a classical one-component system with model interaction potential”, High Temperature, 38:3 (2000), 494

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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