  In this work we study opinion formation in a population participating of a
public debate with two distinct choices. We considered three distinct
mechanisms of social interactions and individuals' behavior: conformity,
nonconformity and inflexibility. The conformity is ruled by the majority-rule
dynamics, whereas the nonconformity is introduced in the population as an
independent behavior, implying the failure to attempted group influence.
Finally, the inflexible agents are introduced in the population with a given
density. These individuals present a singular behavior, in a way that their
stubbornness makes them reluctant to change their opinions. We consider these
effects separately and all together, with the aim to analyze the critical
behavior of the system. We performed numerical simulations in some lattice
structures and for distinct population sizes, and our results suggest that the
different formulations of the model undergo order-disorder phase transitions in
the same universality class of the Ising model. Some of our results are
complemented by analytical calculations.
