Critical Behavior of a Three-State Potts Model on a Voronoi Lattice

Abstract

We use the single-histogram technique to study the critical behavior of the three-state Potts model on a (random) Voronoi-Delaunay lattice with size ranging from 250 to 8000 sites. We consider the effect of an exponential decay of the interactions with the distance,$J(r)=J_0\exp (-ar)$, with $a>0$, and observe that this system seems to have critical exponents $\gamma$ and $\nu$ which are different from the respective exponents of the three-state Potts model on a regular square lattice. However, the ratio $\gamma /\nu$ remains essentially the same. We find numerical evidences (although not conclusive, due to the small range of system size) that the specific heat on this random system behaves as a power-law for $a=0$ and as a logarithmic divergence for $a=0.5$ and $a=1.0$

3 pages, 5 figures

Cited by in corpus (15)

• Majority-vote model on directed Erdos-Renyi random graphs
• Majority-Vote Model on a Random Lattice
• The Harris-Luck criterion for random lattices
• Phase Transitions on Random Lattices: How Random is Topological Disorder?
• Contact process on a Voronoi triangulation
• Majority-vote model on triangular, honeycomb and Kagome lattices
• Nonequilibrium Zaklan model on Apollonian Networks
• Unexpected Spin-Off from Quantum Gravity
• Magnetic models on various topologies
• Directed polymers and interfaces in random media : free-energy optimization via confinement in a wandering tube
• Explosive dismantling of two-dimensional random lattices under betweenness centrality attacks
• Multifractal analysis of electronic states on random Voronoi-Delaunay lattices
• Potts model with $q=4,6,$ and 8 states on Voronoi-Delaunay random lattice
• Potts model with q=3 and 4 states on directed Small-World network
• Universality of continuous phase transitions on random Voronoi graphs