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Related Experiment Videos

High dimensionality as an organizing device for classical fluids.

H L Frisch1, J K Percus

  • 1Chemistry Department, State University of New York at Albany, Albany, New York 12222, USA.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
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In high dimensions, Mayer series for classical fluids diverge but a dominant ring diagram term allows analytic extension. This reveals a second virial approximation remains valid at higher densities, predicting a spinodal and phase transition.

Area of Science:

  • Statistical Mechanics
  • Thermodynamics
  • High-Dimensional Physics

Background:

  • Classical fluids in thermal equilibrium are typically described by Mayer diagrammatic expansions.
  • High-dimensional spaces present unique challenges for these expansions, often leading to divergences.

Purpose of the Study:

  • To reformulate the Mayer expansion for classical pair-interacting fluids in high-dimensional spaces.
  • To analyze the behavior of the series at asymptotic high dimensionality and identify dominant terms.
  • To investigate the implications of these findings for the fluid's equation of state and phase transitions.

Main Methods:

  • Adaptation of the Mayer diagrammatic expansion for high-dimensional systems.
  • Analysis of series convergence and identification of dominant ring diagram contributions.

Related Experiment Videos

  • Analytic extension in density by summing dominant ring terms for hard-core interactions.

    • Main Results:

    • At high dimensions, the Mayer series is dominated by a single ring diagram term.
    • When this term is negative, the series diverges, but analytic extension is possible.
    • A second virial truncation remains valid at densities significantly higher than the divergence point.

    Conclusions:

    • The study provides a method for analytic extension of the Mayer series in high dimensions.
    • Corrections to the equation of state appear near a specific scaled density, indicating a spinodal.
    • The findings suggest a potential phase transition in these systems, offering avenues for further research.