Consensus and transitions in coupled Sznajd networks

In this work we investigate two coupled square lattice networks undergoing Sznajd model dynamics. The coupling between the networks is quantified by a coupling strength $p$. Monte Carlo simulations indicate that the exit probability of each network (to reach either all spins up or all down) depends on $p$ and the initial density of up spins $d$ in the other network. For fixed initial densities, we find a critical coupling $p_c$, above which no further changes in the exit probability are observed. We also find $p_c$ to decrease linearly with increasing $d$. The consensus time scales with system size as $L^{\alpha}$, where $\alpha$ = $\alpha$($p$,$d$). The conditions that must be met for the two networks to reach consensus are also considered.