Universality of continuous phase transitions on random Voronoi graphs

Area of Science:

• Statistical Mechanics
• Complex Systems
• Condensed Matter Physics

Background:

• The Voronoi construction is widely used in science, but its dual, the Delaunay triangulation, has been prioritized in studying critical phenomena.
• Previous research has overlooked the role of Voronoi graphs in statistical mechanics, particularly concerning critical phenomena and phase transitions.

Purpose of the Study:

• To investigate the impact of quenched disorder in random Voronoi graphs on critical phenomena in three distinct statistical mechanics models.
• To determine if the topological disorder of Voronoi graphs influences phase transitions, by isolating it from node-intrinsic coordination number variations.

Main Methods:

• Utilized large-scale numerical simulations to analyze the behavior of the systems.
• Employed finite-size scaling techniques to accurately determine critical points and scaling exponents.
• Focused on three models: the equilibrium spin-1/2 Ising model, the nonequilibrium contact process, and the conserved stochastic sandpile model.

Main Results:

• Demonstrated that all three studied systems, when simulated on random Voronoi graphs, belong to their respective clean universality classes.
• Established that the quenched disorder introduced by the random lattice structure is irrelevant to the character of the phase transitions.
• Reported precise values for critical points and, for the Ising model, the first correction-to-scaling exponent.

Conclusions:

• Quenched disorder from random Voronoi lattices does not alter the fundamental nature of phase transitions in these statistical mechanics systems.
• The study fills a gap in the literature by considering Voronoi constructions in critical phenomena research.
• Confirms the universality of the studied systems despite the presence of lattice disorder.