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Higher orders of self-similar approximations for thermodynamic potentials

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  • Yukalov, V.I.
  • Yukalova, E.P.

Abstract

The problem of calculating thermodynamic potentials in statistical mechanics by using the method of self-similar approximations developed by the authors is considered. An emphasis is made on the search for a regular procedure of defining higher-order terms providing a good accuracy and stability of the method. It is shown how the renormalized perturbation theory can be reformulated to the language of dynamical theory. Then, instead of sequences of approximants one can study trajectories of cascades whose fixed-point attractors play the role of the limits for the corresponding sequences of perturbative terms. As an illustration of the procedure the free energy of a zero-dimensional ϕ4 model is calculated up to the third order of the self-similar approximation whose precision is found to be greater than 0.1% for all coupling parameters ranging from zero to infinity.

Suggested Citation

  • Yukalov, V.I. & Yukalova, E.P., 1994. "Higher orders of self-similar approximations for thermodynamic potentials," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 206(3), pages 553-580.
    • Handle: RePEc:eee:phsmap:v:206:y:1994:i:3:p:553-580
    DOI: 10.1016/0378-4371(94)90324-7
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    1. Yukalov, V.I. & Yukalova, E.P., 1993. "Self-similar approximations for thermodynamic potentials," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 198(3), pages 573-592.
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    Cited by:

    1. Yukalov, V.I. & Yukalova, E.P., 1996. "Evaporation and condensation of clusters," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 223(1), pages 15-33.
    2. Yukalov, V.I. & Yukalova, E.P., 1996. "Temporal dynamics in perturbation theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 225(3), pages 336-362.

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    1. Yukalov, V.I. & Yukalova, E.P., 1996. "Evaporation and condensation of clusters," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 223(1), pages 15-33.
    2. Yukalov, V.I. & Yukalova, E.P., 1997. "Multichannel approach to clustering matter," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 243(3), pages 382-414.
    3. Yukalov, V.I. & Yukalova, E.P., 1996. "Temporal dynamics in perturbation theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 225(3), pages 336-362.

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