Figure 3

The nature of phase transitions. (a,b) The distribution of the order parameter μ derived from \(R=100\) runs. In (a) the noise is comprehension noise and in (b) it is production noise. In the ordered phase, in each run the system goes to one of the two ordered phases. Consequently, the probability distribution of the order parameter has two peaks each corresponding to uninformed or informed consensus phases. By increasing h at fixed \(\eta \), the probability of going to the informed consensus increases, while the probability of going to uninformed consensus phase decreases. These show that the informed-uninformed transition is discontinuous. (c,d) The distribution of the majority size m in the order-disorder transition region, derived from a time series of the system, for comprehension noise (c), and production noise (d). The distribution is bimodal in both cases. By increasing the noise, the peak corresponding to the ordered phase decreases, while that corresponding to the disordered phase increases. This indicates a discontinuous transition.