Area covered by disks in small-bounded continuum percolating systems: An application to the string percolation model

Area of Science:

• High-energy physics
• Statistical mechanics
• String theory

Background:

• The string percolation model studies high-energy particle collisions using 2D continuum percolation theory.
• Systems are typically considered in the thermodynamic limit, often with periodic boundary conditions.

Purpose of the Study:

• To investigate modifications to area coverage in continuum percolating systems with a finite number of disks.
• To analyze the impact of boundary geometry (circle, ellipse, triangle, square, pentagon) on percolation properties.
• To examine the effects of these modifications on string percolation model parameters like color suppression, temperature, and speed of sound.

Main Methods:

• Simulating continuum percolation with a finite number of disks on various bounded geometries.
• Analyzing the fraction of area covered by disks.
• Investigating deviations from thermodynamic limit behavior.
• Calculating corrections to string percolation model parameters.

Main Results:

• The deviation in disk area coverage from the thermodynamic limit exhibits universal behavior, dependent on density, disk number, and boundary shape.
• A damping function, related to finite boundary effects, modifies the color suppression factor.
• Corrections to temperature and speed of sound are derived for small and elliptically bounded systems.

Conclusions:

• Finite boundary effects introduce significant modifications to the string percolation model.
• The observed universal behavior provides a framework for understanding these finite-size corrections.
• These findings are relevant for interpreting experimental data from high-energy particle collisions.