Simulation of majority vote disturbed by power-law noise

Simulations are reported on the Ising two-dimensional ferromagnet in the presence of a special kind of noise. The noise spectrum P(n) follows a power law, where P(n) is the probability of flipping n randomly selected spins at each timestep. This is introduced to mimic the self-organized criticality as a model influence of a complex environment. We reproduced the phase transition in a way that is similar to the 1992 model of de Oliveira. Above some value of the noise amplitude the magnetization tends to zero; otherwise it remains constant after some relaxation. Information of the initial spin orientation remains preserved to some extent by short-range spin-spin correlations. The distribution of the times between flips is exponential. The results are discussed as a step towards modelling of social systems.