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Ising model for the freezing transition.

Jacobo Troncoso1, Claudio A Cerdeiriña1

  • 1Instituto de Física e Ciencias Aeroespaciais da Universidade de Vigo and Unidad MSMN Asociada al CSIC por el IQF Blas Cabrera, Ourense 32004, Spain.

Physical Review. E
|February 17, 2024
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Summary
This summary is machine-generated.

We developed a new Ising model that explains freezing transitions in matter. This model accurately reproduces the van der Waals picture of states of matter using statistical mechanics principles.

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Area of Science:

  • Statistical Mechanics
  • Thermodynamics
  • Condensed Matter Physics

Background:

  • Understanding the fundamental mechanisms of phase transitions, particularly freezing, is crucial in thermodynamics.
  • Existing models often struggle to capture the full complexity of the solid-fluid transition from first principles.

Purpose of the Study:

  • To introduce a novel three-state Ising model incorporating entropy-volume coupling and a packing mechanism.
  • To investigate the thermodynamics of solid and fluid phases and the freezing transition.
  • To reproduce the van der Waals picture of states of matter from statistical mechanics.

Main Methods:

  • Utilizing a three-state Ising model with entropy-volume coupling and a packing mechanism.
  • Employing a grand canonical ensemble where energy, volume, and particle number fluctuate.
  • Applying mean-field theory to analyze model solutions and phase transitions.

Main Results:

  • The model exhibits a first-order phase transition similar to hard-sphere freezing without attractive interactions.
  • Inclusion of attractive interactions allows reproduction of a simple substance's phase diagram, achieving the van der Waals picture.
  • Mean-field theory is shown to be a plausible approach for three-dimensional freezing and suggests persistence in higher dimensions.

Conclusions:

  • The developed Ising model provides a first-principles statistical mechanics explanation for freezing and the van der Waals picture.
  • Mean-field theory offers a reasonable qualitative description of three-dimensional freezing.
  • The model's findings align with recent simulation studies on freezing in extended dimensions.