Gap Statistics for Confined Particles with Power-Law Interactions.

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.