Nonequilibrium Zaklan model on Apollonian Networks

Abstract

The Zaklan model had been proposed and studied recently using the equilibrium Ising model on Square Lattices (SL) by Zaklan et al (2008), near the critica temperature of the Ising model presenting a well-defined phase transition; but on normal and modified Apollonian networks (ANs), Andrade et al. (2005, 2009) studied the equilibrium Ising model. They showed the equilibrium Ising model not to present on ANs a phase transition of the type for the 2D Ising model. Here, using agent-based Monte-Carlo simulations, we study the Zaklan model with the well-known majority-vote model (MVM) with noise and apply it to tax evasion on ANs, to show that differently from the Ising model the MVM on ANs presents a well defined phase transition. To control the tax evasion in the economics model proposed by Zaklan et al, MVM is applied in the neighborhood of the critical noise $q_c$ to the Zaklan model. Here we show that the Zaklan model is robust because this can be studied besides using equilibrium dynamics of Ising model also through the nonequilibrium MVM and on various topologies giving the same behavior regardless of dynamic or topology used here.

11 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:1204.0386 and arXiv:0910.1964

References in corpus (12)

• Statistical physics of social dynamics
• Finite-size scaling in complex networks
• Majority-vote model on hyperbolic lattices
• Majority-vote model on (3,4,6,4) and (3^4,6) Archimedean lattices
• Ising model on the Apollonian network with node dependent interactions
• The phase diagram and critical behavior of the three-state majority-vote model
• Majority-vote model on triangular, honeycomb and Kagome lattices
• q-state Potts model on the Apollonian network
• Blume-Capel model on directed and undirected Small-World Voronoi-Delaunay random lattices
• Non-nequilibrium model on Apollonian networks
• Simulation of majority rule disturbed by power-law noise on directed and undirected Barabasi-Albert networks
• Potts model with $q=4,6,$ and 8 states on Voronoi-Delaunay random lattice

Cited by in corpus (5)

• Ising models on the Regularized Apollonian Network
• The precursor of the critical transitions in majority vote model with the noise feedback from the vote layer
• Majority-vote model with heterogeneous agents on square lattice
• Exactly solvable tight-binding model on the RAN: fractal energy spectrum and Bose-Einstein condensation
• Majority-vote model on Opinion-Dependent Networks