Q-Neighbor Ising model on a polarized network

In this paper, we examine the interplay between the lobby size q in the q-neighbor Ising model of opinion formation [Phys. Rev. E 92, 052105 (2015)1539-375510.1103/PhysRevE.92.052105] and the level of overlap v of two fully connected graphs. Results suggest that for each lobby size q≥3, a specific level of overlap v^{*} exists, which destroys initially polarized clusters of opinions. By performing Monte-Carlo simulations, backed by an analytical approach, we show that the dependence of the v^{*} on the lobby size q is far from trivial in the absence of temperature, showing consecutive maximum and minimum, that additionally depends on the parity of q. The temperature is, in general, a destructive factor; its increase leads to the collapse of polarized clusters for smaller values of v, and additionally brings a substantial decrease in the level of polarization. However, we show that this behavior is counterintuitively inverted for specific lobby sizes and temperature ranges.