Percolation of systems having hyperuniformity or giant number fluctuations

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Complex Systems

Background:

• The Ashkin-Teller model is a significant statistical mechanics model for studying phase transitions.
• Percolation transitions are fundamental phenomena in statistical physics, describing connectivity in disordered systems.
• Understanding hyperuniformity and its relation to critical phenomena is an active research area.

Purpose of the Study:

• To investigate percolation transitions in 2D point configurations generated from the Ashkin-Teller model.
• To analyze the impact of model parameter \( \lambda \) on correlation functions and critical behavior.
• To identify potential superuniversality classes in these configurations.

Main Methods:

• Generating point configurations (PCs) on a square lattice by thresholding local energy in the 2D Ashkin-Teller model.
• Studying percolation transitions by varying the particle density threshold \( \rho \) along the critical Baxter line.
• Analyzing power-law correlations and critical exponents for different values of \( \lambda \).

Main Results:

• Point configurations exhibit power-law correlations with a decay exponent \( \alpha \) independent of \( \rho \) but continuously varying with \( \lambda \).
• For \( \lambda < 0 \), PCs are hyperuniform, and percolation critical behavior mirrors ordinary percolation.
• For \( \lambda > 0 \), configurations show giant number fluctuations, and critical exponents vary continuously, forming a 2D percolation superuniversality class.

Conclusions:

• The study reveals a rich phase diagram for percolation in the Ashkin-Teller model.
• Hyperuniformity in 2D systems does not alter standard percolation critical behavior.
• A novel superuniversality class for 2D percolation is identified in systems with giant number fluctuations.