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Equilibrium states corresponding to targeted hyperuniform nonequilibrium pair statistics.

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The Zhang-Torquato conjecture is supported by findings showing nonequilibrium systems can be replicated by equilibrium models. This research explores hyperuniformity in glass and critical models, revealing insights into system equilibrium and self-assembly.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Soft Matter Systems

Background:

  • The Zhang-Torquato conjecture posits that nonequilibrium systems' properties can be matched by equilibrium systems with effective two-body interactions.
  • Hyperuniformity is an exotic property observed in certain nonequilibrium systems, characterized by suppressed large-scale density fluctuations.

Purpose of the Study:

  • To test the Zhang-Torquato conjecture using singular nonequilibrium models with hyperuniformity.
  • To investigate the structural degeneracy and higher-order statistics of nonequilibrium-equilibrium correspondences.
  • To explore the potential for self-assembly of tunable hyperuniform soft-matter systems.

Main Methods:

  • Studied two nonequilibrium models: a 2D perfect glass and a 3D critical absorbing-state model.
  • Computed pair correlation functions, structure factors, and higher-order statistics (hole probability).
  • Analyzed effective potentials and inherent structures after quenching.

Main Results:

  • Nonequilibrium models (2D glass, 3D critical) were accurately reproduced by equilibrium states with effective one- and two-body potentials.
  • Higher-order statistics, particularly hole probability, distinguished between equilibrium and nonequilibrium systems, serving as a measure of deviation from equilibrium.
  • All studied systems exhibited the bounded-hole property, with hyperuniform systems showing rarer large holes than simple lattices.

Conclusions:

  • The findings provide strong support for the Zhang-Torquato conjecture.
  • Higher-order statistics offer a quantitative measure of a system's departure from equilibrium.
  • The developed methods can aid in the design and self-assembly of novel hyperuniform soft-matter materials.