  We study how the opinions of a group of individuals determine their spatial
distribution and connectivity, through an agent-based model. The interaction
between agents is described by a Potts-like Hamiltonian in which agents are
allowed to move freely without an underlying lattice (the average network
topology connecting them is determined from the parameters). This kind of model
was derived using maximum entropy statistical inference under fixed expectation
values of certain probabilities that (we propose) are relevant to social
organization. Control parameters emerge as Lagrange multipliers of the maximum
entropy problem, and they can be associated with the level of consequence
between the personal beliefs and external opinions, and the tendency to
socialize with peers of similar or opposing views. These parameters define a
phase diagram for the social system, which we studied using Monte Carlo
Metropolis simulations. Our model presents both first and second-order phase
transitions, depending on the ratio between the internal consequence and the
interaction with others. We have found a critical value for the level of
internal consequence, below which the personal beliefs of the agents seem to be
irrelevant.
