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Summary
This summary is machine-generated.

Disordered systems exhibit step-wise responses due to energy minima. This study uses probabilistic methods to analyze static avalanches in mean-field systems, finding conditions for power-law behavior.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Complex Systems

Background:

  • Disordered systems possess numerous local energy minima, leading to abrupt responses under perturbation.
  • Replica symmetry breaking is a key concept in understanding the complex behavior of these systems.

Purpose of the Study:

  • To compute the complete probability distribution of static avalanches in mean-field disordered systems.
  • To identify conditions governing power-law behavior in avalanche distributions under small perturbations.

Main Methods:

  • Utilizing elementary probabilistic methods to analyze systems described by replica symmetry breaking.
  • Calculating the full probability distribution of static avalanches.

Main Results:

  • A precise condition for power-law behavior in avalanche distributions was determined.
  • Predictions align well with existing theoretical results.
  • Simulations of 3D soft sphere systems at jamming and higher densities validate the findings.

Conclusions:

  • The probabilistic approach effectively characterizes static avalanches in disordered systems.
  • The identified condition for power-law behavior is a significant finding for understanding system responses.
  • The results offer a unified perspective on jamming and related phenomena in soft matter.