The shortest-graph method for calculation of the pair-correlation function in crystalline systems.

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Computational Materials Science

Background:

• Accurate calculation of the pair correlation function g(r) is crucial for understanding crystalline systems.
• Existing methods may be computationally intensive or less accurate for certain crystal structures.

Purpose of the Study:

• To introduce a new, efficient method for approximating the pair correlation function g(r) in crystalline systems.
• To validate the proposed method against established simulation techniques.

Main Methods:

• The method approximates g(r) by considering only the shortest lattice graph connections between particles.
• It accounts for particle delocalization by focusing on these primary interactions.
• The approach was tested on Lennard-Jones and Yukawa crystalline systems.

Main Results:

• The proposed method shows excellent agreement with molecular dynamics simulations.
• Accuracy is maintained up to the melting line for the tested systems.
• The method effectively captures the structural properties of simple crystals.

Conclusions:

• The new method provides a computationally efficient and accurate way to approximate g(r) in crystalline systems.
• It is applicable to simple crystals like colloids and plasma crystals.
• The method has potential for generalization to systems with anisotropic interactions.