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O B Eriçok1, K Ganesan1, J K Mason1

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Hard sphere systems reveal phase transition insights. Critical configurations in their configuration space change dramatically, indicating the onset of first-order phase transitions in simple fluids.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Computational Physics

Background:

  • Hard sphere systems model simple fluids and their phase transitions.
  • Configuration spaces of hard spheres in a 3D torus modulo symmetry groups offer insights into phase transitions.
  • Topological changes in configuration space are conjectured to relate to first-order phase transitions.

Purpose of the Study:

  • To investigate the relationship between topological changes in hard sphere configuration spaces and phase transitions.
  • To sample critical configurations for 1 to 12 spheres using Morse theory.
  • To analyze the topological and geometric properties of configuration spaces for hard sphere systems.

Main Methods:

  • Morse-theoretic approach to sample critical configurations.
  • Construction of explicit triangulations for configuration spaces.
  • Analysis of configuration space diameter using commute time and diffusion distances.

Main Results:

  • Critical configurations associated with geometric changes that connect distant regions and reduce configuration space diameter.
  • Number of critical configurations increases exponentially with the number of spheres.
  • A database of critical configurations for 1 to 12 spheres is available online.

Conclusions:

  • The onset of first-order phase transitions in hard sphere systems is linked to geometric changes in configuration space.
  • The exponential increase in critical configurations suggests a discontinuity in configuration space diameter at the thermodynamic limit.
  • This study provides a computational framework for understanding fluid phase transitions through configuration space topology.