A new model is proposed, in the context of Axelrod's model for the study of cultural dissemination, to include an external vector field (VF) which describes the effects of mass media on social systems. The VF acts over the whole system and it is characterized by two parameters: a nonnull overlap with each agent in the society and a confidence value of its information. Beyond a threshold value of the confidence, there is induced monocultural globalization of the system lined up with the VF. Below this value, the multicultural states are unstable and certain homogenization of the system is obtained in opposite line up according to that we have called negative publicity effect. Three regimes of behavior for the spread process of the VF information as a function of time are reported.