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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. Zakharova, I. K. Loktionovb

a Novgorod State University after Yaroslav the Wise
b Donetsk National Technical University
References:
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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\paper Classical statistics of one-component systems with model potentials
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\pages 167--176
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\transl
\jour Theoret. and Math. Phys.
\yr 1999
\vol 119
\issue 1
\pages 532--539
\crossref{https://doi.org/10.1007/BF02557350}
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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:
    1. V. B. Bobrov, “On the closed interpolation equation of state for a simple liquid”, High Temperature, 61:3 (2023), 320–327  mathnet  mathnet  crossref  crossref
    2. I. K. Loktionov, “Equation of state for a liquid with double exponential potential”, High Temperature, 59:2 (2021), 148–155  mathnet  crossref  crossref  isi  elib
    3. 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  crossref  isi
    4. Budkov Yu.A., “Statistical Field Theory of Ion-Molecular Solutions”, Phys. Chem. Chem. Phys., 22:26 (2020), 14756–14772  crossref  isi
    5. 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  crossref  isi  scopus
    6. 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  mathnet  crossref  crossref  isi  elib
    7. 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  crossref  isi
    8. 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  crossref
    9. 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  mathnet  crossref  crossref  isi  elib  elib
    10. 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  mathnet  crossref  isi  elib  elib
    11. 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  mathnet  crossref  isi  elib
    12. Loktionov I.K., “Teplofizicheskie svoistva sistem s chetyrekhparametricheskim ostsilliruyuschim potentsialom vzaimodeistviya”, Ultrazvuk i termodinamicheskie svoistva veschestva, 2012, no. 38, 49–53  elib
    13. 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  elib
    14. I. K. Loktionov, “Thermodynamic Properties of One-Component Systems with Pair Two-Parameter Interaction Potentials”, High Temperature, 49:4 (2011), 512–519  mathnet  crossref  isi  elib
    15. Zakharov, AY, “Ensembles in classical statistical mechanics and their unification via nonlinear field theory”, International Journal of Quantum Chemistry, 100:4 (2004), 442  crossref  mathscinet  isi  scopus  scopus  scopus
    16. Zakharov, AY, “Intermolecular forces and random fields: Mutual renormalizations in classical statistical mechanics”, International Journal of Quantum Chemistry, 96:3 (2004), 234  crossref  isi  scopus  scopus  scopus
    17. Zakharov, AY, “Quasi-particles, random fields, and phase transitions in classical statistical mechanics”, Russian Journal of Physical Chemistry, 77 (2003), S1  isi
    18. Zakharov, AY, “The concept of elementary excitations in classical statistical mechanics”, Technical Physics Letters, 27:7 (2001), 560  crossref  adsnasa  isi  scopus  scopus  scopus
    19. Loktionov, IK, “One-dimensional classical model with phase transition”, High Temperature, 39:2 (2001), 325  mathnet  mathnet  crossref  isi  scopus  scopus  scopus
    20. Loktionov, IK, “Determination of the critical parameters of a classical one-component system with model interaction potential”, High Temperature, 38:3 (2000), 494  mathnet  mathnet  crossref  isi  scopus  scopus  scopus
    Citing articles in Google Scholar: Russian citations, English citations
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    Теоретическая и математическая физика Theoretical and Mathematical Physics
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