Effects of disorder on Harris-criterion violating percolation

Area of Science:

• Physics
• Statistical Mechanics
• Computational Physics

Background:

• The Harris criterion predicts how impurities affect critical behavior during phase transitions.
• Protected percolation is a model system that may violate the Harris criterion.
• Understanding the role of impurities is crucial for characterizing phase transitions in disordered systems.

Purpose of the Study:

• To investigate whether critical exponents in protected percolation are altered by impurities.
• To test the validity of the Harris criterion in protected percolation models.
• To compare the effects of impurities on 2D and 3D protected percolation systems.

Main Methods:

• Computer simulations were employed to model protected percolation systems.
• Impurities were introduced in the form of missing sites and immortal sites.
• Critical exponents were calculated for systems with and without impurities.

Main Results:

• Critical exponents for 3D protected percolation changed significantly with the introduction of impurities.
• Impurities did not alter the critical exponents for 2D protected percolation.
• Standard percolation in 2D also showed stability against impurities.

Conclusions:

• Protected percolation in three dimensions violates the Harris criterion.
• Two-dimensional protected percolation and standard percolation are robust against site impurities.
• The dimensionality of the system plays a critical role in the impact of impurities on critical behavior.