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S Santra1, J Kethepalli1, S Agarwal2

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Summary
This summary is machine-generated.

We studied particle gap fluctuations in a Riesz gas with power-law interactions. The gap variance scales with particle number N, and we determined this scaling

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Mathematical Physics

Background:

  • The N-particle classical Riesz gas with power-law interaction 1/r^k is a versatile model.
  • It encompasses systems like Dyson's log-gas, Calogero-Moser model, 1D plasma, and hard-rod gas.
  • Previous studies focused on large-N field theory and average density profiles.

Purpose of the Study:

  • Investigate fluctuations in the Riesz gas system.
  • Analyze the statistics of the gap between successive particles.
  • Determine the system size scaling of gap distributions.

Main Methods:

  • Direct Monte Carlo simulations to study gap statistics.
  • Microscopic Hessian calculations for theoretical support.
  • Quadratic field theory approach for analysis.

Main Results:

  • The variance of particle gaps scales as N^{-b_k}.
  • The k-dependence of the scaling exponent b_k was determined.
  • Gap distributions and their system size scaling were computed.
  • Scaling behavior was observed for k > -2, except for -1 < k < 0.

Conclusions:

  • The study provides insights into the fluctuation properties of the Riesz gas.
  • Scaling behavior of gap distributions is a key finding across various interaction strengths.
  • The results offer a deeper understanding of systems with power-law interactions.