Majority-vote model in one-dimensional on directed small-world networks

In 1992 Oliveira9 proposed the a non-equilibrium model known as MVM which disobeys the detailed balance. The update of the MVM follows a Markov sequence of stochastic dynamics with local rules and with up-down symmetry. In 2D, on a square lattice, the MVM presents a continuous phase transition with critical exponents identical9 of the Ising model10. Sousa11 and Brenda12 studied the Ising model and MVM on DSW random lattices, respectively. The exponents obtained in both models are identical and in agreement with the conjecture suggested by Grinstein et al.1