Scale-free crystallization of two-dimensional complex plasmas: Domain analysis using Minkowski tensors

Area of Science:

• Plasma Physics
• Materials Science
• Statistical Mechanics

Background:

• Complex plasmas offer a unique system for studying phase transitions.
• A recently developed "fractal-domain-structure" (FDS) theory proposes scale-free properties in crystallization.
• Previous analyses used dislocation counting and bond-order metrics, showing preliminary support for FDS.

Purpose of the Study:

• To rigorously test the scale-free phase transition theory (FDS) in two-dimensional complex plasmas.
• To verify the predicted scale-free power-law relation between defect number fraction and system energy.
• To explore the fractal relationship between crystalline domain area and boundary length.

Main Methods:

• Experimental analysis of recrystallization processes in two-dimensional complex plasmas.
• Application of Minkowski tensor methods for morphological analysis of lattice structure.
• Extension of bond-order metric to measure defect number fraction.

Main Results:

• The fractal-domain-structure (FDS) theory is rigorously confirmed, with predictions reproduced exceptionally well.
• A scale-free power-law relation between defect fraction and system energy was verified over an extended range.
• The fractal relationship between domain area and circumference was found to be independent of experimental parameters, suggesting inherent properties of 2D plasma phase transitions.

Conclusions:

• The FDS theory provides a robust framework for understanding phase transitions in complex plasmas.
• Minkowski tensor analysis is a powerful tool for investigating crystallization, revealing nonlinear topological properties.
• The fractal nature of domain-boundary relationships is a fundamental aspect of 2D complex plasma crystallization.