Exact solution of the isotropic majority-vote model on complete graphs.

The isotropic majority-vote (MV) model, which, apart from the one-dimensional case, is thought to be nonequilibrium and violating the detailed balance condition. We show that this is not true when the model is defined on a complete graph. In the stationary regime, the MV model on a fully connected graph fulfills the detailed balance and is equivalent to the modified Ehrenfest urn model. Using the master equation approach, we derive the exact expression for the probability distribution of finding the system in a given spin configuration. We show that it only depends on the absolute value of magnetization. Our theoretical predictions are validated by numerical simulations.

[1]  Francisco W. De Sousa Lima,et al.  Phase Transitions in Equilibrium and Non-Equilibrium Models on Some Topologies , 2016, Entropy.

[2]  Andrzej Krawiecki,et al.  Majority-Vote Model on Scale-Free Hypergraphs , 2015 .

[3]  Haifeng Zhang,et al.  Critical noise of majority-vote model on complex networks. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  T. Tomé,et al.  Stochastic Dynamics and Irreversibility , 2014 .

[5]  F. Sastre,et al.  Critical phenomena in the majority voter model on two-dimensional regular lattices. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  F. Sastre,et al.  Critical phenomena of the majority voter model in a three-dimensional cubic lattice. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Paulo F. C. Tilles,et al.  Mean-field analysis of the majority-vote model broken-ergodicity steady state , 2012, 1203.0162.

[8]  K. Malarz,et al.  Majority-vote model on triangular, honeycomb and Kagomé lattices , 2010, 1007.0739.

[9]  Wooseop Kwak,et al.  Existence of an upper critical dimension in the majority voter model. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  In-mook Kim,et al.  Critical behavior of the majority voter model is independent of transition rates. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  F. Moreira,et al.  Majority-vote model on random graphs. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  M. J. Oliveira,et al.  Nonequilibrium spin models with Ising universal behaviour , 1993 .

[13]  Grinstein,et al.  Statistical mechanics of probabilistic cellular automata. , 1985, Physical review letters.

[14]  M. A. Santosi,et al.  Non-equilibrium spin models with Ising universal behaviour , 2002 .

[15]  M. J. Oliveira,et al.  Isotropic majority-vote model on a square lattice , 1992 .