Information diversity and anomalous scaling in asymmetric social contagion process on low-dimensional static networks

To understand how competition affects the diversity of information, we study the social contagion model introduced by Halvorsen-Pedersen-Sneppen (HPS) [G. S. Halvorsen, B. N. Pedersen, and K. Sneppen, Phys. Rev. E 103, 022303 (2021)2470-004510.1103/PhysRevE.103.022303] on one-dimensional (1D) and two-dimensional (2D) static networks. By mapping the information value to the height of the interface, we find that the width W(N,t) does not satisfy the well-known Family-Vicsek finite-size scaling ansatz. From the numerical simulations, we find that the dynamic exponent z should be modified for the HPS model. For 1D static networks, the numerical results show that the information landscape is always rough with an anomalously large growth exponent, β. Based on the analytic derivation of W(N,t), we show that the constant small number of influencers created for unit time and the recruitment of new followers are two processes responsible for the anomalous values of β and z. Furthermore, we also find that the information landscape on 2D static networks undergoes a roughening transition, and the metastable state emerges only in the vicinity of the transition threshold.