2025/06/06 by Muslim, Roni, Kim, Jihye, Oikawa, Noriko +2 · 2 citations
#FOS: Physical sciences #Physics and Society (physics.soc-ph)
paper · doi:10.48550/arxiv.2506.05669
We investigate a variant of the two-state q-voter model in which agents update their states under a random external field (which points upward with probability s and downward with probability 1-s) with probability p or adopt the unanimous opinion of q randomly selected neighbors with probability 1-p. Using mean-field analysis and Monte Carlo simulations, we identify an order-disorder transition at pc when s=\tfrac12. Notably, in the regime of p>pc, we estimate the time for systems to reach disordered state from consensus state and find the logarithmic scaling Tdis ∼ Bln N, with B = 1/(2p) for q = 1, while for q > 1, B depends on both p > pc and q. We observe that disordering dynamics slow down significantly for nonlinear strengths q between 2 and 3, independent of the probability p. On the other hand, when s=0 or s=1, the system is bound to reach consensus, with the consensus time scaling logarithmically with system size as Tcon ∼ Bln N, where B = 1/p for q = 1 and B = 1 for q > 1. Furthermore, in the limit of p = 0, we derive a closed-form exit probability valid for arbitrary values of q and demonstrate a finite-size scaling collapse. These results clarify how external cues and peer conformity jointly control ordering and disordering in binary opinion dynamics.