Figure 4. Equilibrium mean field behavior when zealots favor the state x and α = 2.

The disorder-order transition becomes less abrupt as more zealots occupy the state x, Φ = 0.03 (a) and Φ = 0.10 (b). The zealots create a bias in the global opinion toward x, destroying the symmetry of the model dynamics in the absence of zealots (black, dash-dot lines). A stable majority in x (red, solid line) exists for all values of K, while a stable majority in z (blue, solid line) exists only for high K values. The unstable equilibrium (green, dashed line) dividing the two regimes is shifted to negative values. The analytical prediction (lines) given by the solution to Eq. (31) agrees with numerical simulation of the model (circles) with N = 1000, g = 0.01, and the values (m_x, m_y, m_z) set to (50, 30, 20) in (a) and (100, 0, 0) in (b).