  The competitive balance model was proposed as an extension of the structural
balance theory, aiming to account for heterogeneities observed in real-world
networks. In this model, different paradigms lead to form different friendship
and enmity. As an example, friendship or enmity between countries can have a
political or religious basis. The suggested Hamiltonian is symmetrical between
paradigms. Our analyses show that a balanced state can be achieved if just one
paradigm prevails in the network and the paradigm shift is possible only by
imposing an external field. In this paper, we investigate the influence of the
external field on the evolution of the network. We drive the mean-field
solutions of the model and verify the accuracy of our analytical solutions by
performing Monte-Carlo simulations. We observe that the external field breaks
the symmetry of the system. The response of the system to this external field,
contingent upon temperature, can be either paramagnetic or ferromagnetic. We
observed a hysteresis behavior in the ferromagnetic regime. Once communities
are formed based on a certain paradigm, then they resist change. We found that
to avoid wasting energy we need to know the level of stochastic behavior in the
network. Analogous to magnetic systems, we observe that susceptibility adheres
to Curie's law.
