Majorityvote model on hyperbolic lattices
Abstract
We study the critical properties of a nonequilibrium statistical model, the majorityvote model, on heptagonal and dual heptagonal lattices. Such lattices have the special feature that they only can be embedded in negatively curved surfaces. We find, by using Monte Carlo simulations and finitesize analysis, that the critical exponents 1/ν , β/ν , and γ/ν are different from those of the majorityvote model on regular lattices with periodic boundary condition, which belongs to the same universality class as the equilibrium Ising model. The exponents are also from those of the Ising model on a hyperbolic lattice. We argue that the disagreement is caused by the effective dimensionality of the hyperbolic lattices. By comparative studies, we find that the critical exponents of the majorityvote model on hyperbolic lattices satisfy the hyperscaling relation 2β/ν+γ/ν=D_{eff} , where D_{eff} is an effective dimension of the lattice. We also investigate the effect of boundary nodes on the ordering process of the model.
 Publication:

Physical Review E
 Pub Date:
 January 2010
 DOI:
 10.1103/PhysRevE.81.011133
 arXiv:
 arXiv:0911.0049
 Bibcode:
 2010PhRvE..81a1133W
 Keywords:

 05.50.+q;
 02.40.Ky;
 64.60.Cn;
 05.70.Ln;
 Lattice theory and statistics;
 Riemannian geometries;
 Orderdisorder transformations;
 statistical mechanics of model systems;
 Nonequilibrium and irreversible thermodynamics;
 Condensed Matter  Statistical Mechanics;
 Physics  Physics and Society
 EPrint:
 8 pages, 9 figures