Majorityvote model on triangular, honeycomb and Kagomé lattices
Abstract
On Archimedean lattices, the Ising model exhibits spontaneous ordering. Three examples of these lattices of the majorityvote model with noise are considered and studied through extensive Monte Carlo simulations. The order/disorder phase transition is observed in this system. The calculated values of the critical noise parameter are q_{c}=0.089(5), q_{c}=0.078(3), and q_{c}=0.114(2) for honeycomb, Kagomé and triangular lattices, respectively. The critical exponents β/ν, γ/ν and 1/ν for this model are 0.15(5), 1.64(5), and 0.87(5); 0.14(3), 1.64(3), and 0.86(6); 0.12(4), 1.59(5), and 1.08(6) for honeycomb, Kagomé and triangular lattices, respectively. These results differ from the usual Ising model results and the majorityvote model on sofar studied regular lattices or complex networks. The effective dimensionalities of the system D=1.96(5) (honeycomb), D=1.92(4) (Kagomé), and D=1.83(5) (triangular) for these networks are just compatible to the embedding dimension two.
 Publication:

Physica A Statistical Mechanics and its Applications
 Pub Date:
 January 2011
 DOI:
 10.1016/j.physa.2010.08.054
 arXiv:
 arXiv:1007.0739
 Bibcode:
 2011PhyA..390..359S
 Keywords:

 Condensed Matter  Statistical Mechanics
 EPrint:
 5 pages, 5 figures, RevTeX4