Simulation of majority rule disturbed by power-law noise

TL;DR

This paper investigates how power-law distributed noise affects the phase transition and magnetization in a 2D Ising model, providing insights into complex environmental influences and social system modeling.

Contribution

It introduces a novel noise model with power-law spectrum into the Ising model, exploring its effects on phase transition and spin dynamics.

Findings

Magnetization tends to zero above a certain noise amplitude.

Short-range correlations preserve initial spin information.

Flip time distribution is exponential.

Abstract

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 randomly selected n 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 similar to the case of P(n) = constant. Above some value of the noise amplitude the magnetisation 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 modeling of social systems.