One-component plasma of a million particles via angular-averaged Ewald potential: A Monte Carlo study

Area of Science:

• Plasma Physics
• Computational Physics
• Statistical Mechanics

Background:

• The one-component plasma (OCP) model is fundamental in understanding systems with long-range interactions.
• Accurate calculation of OCP energy is crucial for various physical systems, including electron gases.
• Traditional Ewald potentials can be computationally intensive for large-scale simulations.

Purpose of the Study:

• To derive a correct and computationally efficient expression for the OCP energy using a novel angular-averaged Ewald potential (AAEP).
• To establish a unified approach for determining the thermodynamic limit across a wide range of coupling parameters.
• To demonstrate the computational advantages of the AAEP over traditional methods.

Main Methods:

• Derivation of the AAEP based on the original Ewald potential for OCP.
• Determination of a key constant in the AAEP using cluster expansion in the weak coupling limit.
• Extensive Monte Carlo simulations of OCP with up to one million particles using the AAEP.

Main Results:

• The AAEP provides a simple and effective form suitable for numerical simulations.
• Monte Carlo simulations using AAEP were at least two orders of magnitude faster than those with the traditional Ewald potential.
• The derived unified approach for thermodynamic limit determination proved effective across the investigated coupling range.

Conclusions:

• The AAEP offers a significant improvement in computational efficiency for OCP simulations.
• The AAEP is a valuable tool for path integral Monte Carlo simulations of the uniform electron gas.
• Results align well with theoretical predictions for weakly coupled OCP and prior simulation data.