Majority-vote model on spatially embedded networks: Crossover from mean-field to Ising universality classes
| Autor: | André A. Moreira, F. G. B. Moreira, C. I. N. Sampaio Filho, J. S. Andrade, T. B. dos Santos |
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| Rok vydání: | 2016 |
| Předmět: |
Phase transition
Statistical Mechanics (cond-mat.stat-mech) Crossover FOS: Physical sciences Renormalization group 01 natural sciences 010305 fluids & plasmas Universality (dynamical systems) Mean field theory 0103 physical sciences Exponent Ising model Statistical physics 010306 general physics Critical exponent Condensed Matter - Statistical Mechanics Mathematics |
| Zdroj: | Physical Review E. 93 |
| ISSN: | 2470-0053 2470-0045 |
| DOI: | 10.1103/physreve.93.052101 |
| Popis: | We study through Monte Carlo simulations and finite-size scaling analysis the nonequilibrium phase transitions of the majority-vote model taking place on spatially embedded networks. These structures are built from an underlying regular lattice over which long-range connections are randomly added according to the probability, $P_{ij}\sim{r^{-\alpha}}$, where $r_{ij}$ is the Manhattan distance between nodes $i$ and $j$, and the exponent $\alpha$ is a controlling parameter [J. M. Kleinberg, Nature 406, 845 (2000)]. Our results show that the collective behavior of this system exhibits a continuous order-disorder phase transition at a critical parameter, which is a decreasing function of the exponent $\alpha$. Precisely, considering the scaling functions and the critical exponents calculated, we conclude that the system undergoes a crossover among distinct universality classes. For $\alpha\le3$ the critical behavior is described by mean-field exponents, while for $\alpha\ge4$ it belongs to the Ising universality class. Finally, in the region where the crossover occurs, $3 Comment: 6 pages, 6 figures |
| Databáze: | OpenAIRE |
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