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Thomson problem in the disk.
1Facultad de Ciencias, CUICBAS, Universidad de Colima, Bernal Díaz del Castillo 340, Colima, Colima, Mexico.
Physical Review. E
|December 20, 2023
Summary
We developed a new algorithm to efficiently find the lowest energy states for many interacting charges in a disk. This method significantly reduces computation, enabling studies of larger systems and revealing complex defect structures.
Area of Science:
- Computational Physics
- Condensed Matter Physics
- Statistical Mechanics
Background:
- Understanding the behavior of many-body systems is crucial in physics.
- The Coulomb potential governs interactions between charged particles.
- Finding the ground state (lowest energy configuration) is computationally challenging.
Purpose of the Study:
- To develop an efficient algorithm for determining the classical ground state of charges in a disk.
- To enable the study of larger systems than previously possible.
- To investigate the emergence of topological defects in these systems.
Main Methods:
- Developed an algorithm focusing on peripheral charges to reduce computational complexity.
- Implemented a divide and conquer approach for large-scale simulations.
- Analyzed configurations with up to N=40886 charges.
Main Results:
- The algorithm successfully reduces computational complexity by controlling border charges.
- Enabled simulations of significantly larger charge configurations.
- Observed an increasing richness of topological defect structures with system size.
Conclusions:
- The developed algorithm is effective for finding ground states of Coulomb systems.
- The study demonstrates a scalable approach for complex many-body problems.
- Larger systems exhibit more intricate topological defect patterns.
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