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Cluster self-assembly condition for arbitrary interaction potentials.

Alejandro Mendoza-Coto1, Rômulo Cenci, Guido Pupillo

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We found a mathematical condition predicting when interacting particles form cluster crystals instead of simple lattices. This criterion applies to various repulsive interactions, generalizing previous findings.

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Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Materials Science

Background:

  • Understanding emergent phases in interacting particle systems is crucial for materials design.
  • Previous studies focused on specific bounded potentials for cluster crystal formation.
  • A generalized criterion for arbitrary repulsive potentials is needed.

Purpose of the Study:

  • To establish a sufficient criterion for the emergence of cluster phases in classical particle systems.
  • To identify key characteristics of interaction potentials favoring cluster crystals over triangular lattices.
  • To generalize existing criteria to a broader range of repulsive potentials.

Main Methods:

  • Zero-temperature, low-density analysis of interacting classical particles.
  • Derivation of a mathematical condition based on Fourier components of a regularized interaction potential.
  • Application and verification of the criterion using bounded and unbounded potentials.

Main Results:

  • A novel analytic criterion for self-assembled cluster crystal formation was developed.
  • The criterion successfully predicts cluster crystal emergence for various potentials.
  • The method generalizes known results for bounded potentials to arbitrary repulsive interactions.

Conclusions:

  • The derived criterion provides a robust tool for predicting cluster phase formation.
  • This work extends the understanding of self-assembly in classical particle systems.
  • The findings have implications for designing materials with specific emergent properties.