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Long-range correlations in pinned athermal networks.

Debankur Das1, Pappu Acharya1, Kabir Ramola1

  • 1Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, Hyderabad 500107, India.

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Summary
This summary is machine-generated.

External pinning forces in 2D athermal networks cause long-range displacement correlations. Uncorrelated forces lead to system-size-dependent correlations, verified by simulations.

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Area of Science:

  • Physics
  • Materials Science
  • Statistical Mechanics

Background:

  • Athermal systems lack thermal fluctuations, making their mechanical response unique.
  • Understanding displacement fields is crucial for predicting material behavior under stress.
  • Pinning forces are common in disordered materials and affect their macroscopic properties.

Purpose of the Study:

  • To derive exact results for displacement fields in 2D athermal networks under external pinning forces.
  • To investigate the spatial decay of displacement fields and their correlations.
  • To explore the influence of uncorrelated forces on system-wide displacements.

Main Methods:

  • Developed a Green's function formalism for a triangular lattice with soft potentials.
  • Analyzed displacement fields produced by localized external forces.
  • Extended the formalism to study correlations in displacement fields.
  • Performed numerical simulations to verify theoretical predictions.

Main Results:

  • Derived exact results for displacement fields in response to localized forces.
  • Showed that displacement fields decay as 1/r in the continuum limit from a force dipole.
  • Demonstrated that uncorrelated pinning forces induce long-range correlations in displacements.
  • Identified a nontrivial system size dependence for these correlations.

Conclusions:

  • The study provides exact analytical results for displacement fields in 2D athermal networks.
  • Uncorrelated external forces can lead to emergent long-range order in these systems.
  • Theoretical predictions are validated by numerical simulations, confirming the model's accuracy.