The external field effect on the opinion formation based on the majority rule and the <i>q</i>-voter models on the complete graph

We investigate the external field effect on opinion formation based majority rule and $q$-voter models a complete graph. The can be considered as mass media in social system, with probability $p$ agents following opinion. Based our Monte Carlo simulation, is not strong enough to make system reach homogeneous state (complete consensus) magnetization $m = 1$ for all values of $p$, indicates that existence usual phase transition $p$. In model, eliminates at $p \approx 0.21$. obtain model's critical point scaling parameters using finite-size analysis both have same parameters. decreases models' relaxation time power-law relation such $\tau \sim N^{\beta}$, where $N$ population size, $\beta$ depends follows linear relation, relation.