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Gabriele Costa1, Santi Prestipino1

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Summary
This summary is machine-generated.

We developed a discrete statistical model on a complex polyhedron, revealing sharp phase transitions and unique structures. Monte Carlo simulations showed hysteresis near zero temperature, indicating simulation challenges.

Keywords:
lattice-gas modelsself-assemblyspherical boundary conditions

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Area of Science:

  • Statistical Mechanics and Computational Physics
  • Condensed Matter Theory
  • Discrete Systems Modeling

Background:

  • Discrete statistical systems simplify microstate enumeration compared to continuum systems.
  • Lattice-gas models are crucial for understanding phase transitions and emergent structures.
  • Polyhedral structures offer unique geometric constraints for physical models.

Purpose of the Study:

  • To introduce and analyze a novel lattice-gas model on a pentakis icosidodecahedron.
  • To determine the exact phase diagram and explore diverse interaction patterns.
  • To investigate the low-temperature phases and their structural characteristics.

Main Methods:

  • Exact phase diagram determination using the Wang-Landau method.
  • Exploration of interaction patterns including soft repulsion, Lennard-Jones-like, and SALR potentials.
  • Monte Carlo simulations to reproduce the equation of state and identify dynamic behaviors.

Main Results:

  • Identification of sharp phase transitions at low temperatures.
  • Observation of distinct low-temperature phases: regular polyhedral, cluster-crystal-like, and worm-like structures.
  • Discovery of hysteretic behavior near zero temperature in Monte Carlo simulations, suggesting dynamic bottlenecks.

Conclusions:

  • The discrete lattice-gas model on a complex polyhedron exhibits rich phase behavior.
  • The Wang-Landau method successfully mapped the exact phase diagram.
  • Metropolis dynamics face challenges (hysteretic behavior) near phase transitions at low temperatures.