Phase transitions on random lattices: how random is topological disorder?

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Complex Systems

Background:

• Phase transitions are fundamental in physics, but their behavior on disordered systems remains challenging.
• Existing criteria, like the Harris criterion, often fail for random lattices.
• Topological disorder, specifically lattice connectivity, presents unique challenges.

Purpose of the Study:

• To investigate the impact of topological disorder on phase transitions.
• To develop new criteria for understanding critical phenomena in random systems.
• To explain discrepancies observed in previous studies of random lattices.

Main Methods:

• Theoretical analysis of disorder fluctuations in random lattices.
• Derivation of a novel wandering exponent: ω=(d-1)/(2d).
• Modification of the Imry-Ma criterion for first-order transitions.
• Computer simulations on random Voronoi and other lattices.

Main Results:

• Topological disorder is less relevant than generic randomness for critical point stability.
• The stability criterion is modified to (d+1)ν>2.
• First-order phase transitions are shown to persist in all dimensions d>1.
• Computer simulations validate the theoretical predictions.

Conclusions:

• The study provides a unified explanation for puzzling phase transition behaviors on random lattices.
• The findings offer a more accurate framework for analyzing disordered systems.
• The modified criteria have broad implications for understanding equilibrium and nonequilibrium transitions.