Violation of the Harris-Barghathi-Vojta Criterion

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Materials Science

Background:

• The Harris criterion (1974) predicts stability of continuous phase transitions against quenched disorder if dν > 2.
• The modified Harris criterion (Barghathi & Vojta) for disordered systems is aν > 1, where 'a' is the disorder decay exponent.
• Violations of these criteria have been observed in systems like Voronoi-Delaunay triangulations.

Purpose of the Study:

• To investigate the stability of phase transitions in a novel topologically disordered lattice.
• To test the validity of the modified Harris criterion in systems with slow disorder decay.
• To identify systems that preserve clean universal behavior despite significant topological disorder.

Main Methods:

• Construction and analysis of a specific topologically disordered lattice model.
• Characterization of coordination number fluctuations and their decay exponent 'a'.
• Evaluation of the system's critical behavior and comparison with theoretical criteria.

Main Results:

• The studied lattice exhibits coordination number fluctuations decaying as slowly as conventional uncorrelated randomness (small 'a').
• Despite slow disorder decay, the system preserves clean universal behavior, violating the modified Harris criterion (aν > 1).
• This demonstrates a scenario where topological disorder does not destabilize phase transitions as predicted.

Conclusions:

• The modified Harris criterion is not universally applicable to all topologically disordered systems.
• Topologically disordered systems can exhibit preserved clean universal behavior even with slow disorder decay.
• Further theoretical and experimental work is needed to understand the limits of these criteria.