Geometrical distribution of agents based on a generalised Potts model

In collective local interaction systems with agents assigned to different profiles (categories, traits), the distribution of such profiles in the neighbourhood of any agent affects the exchange of ideas, a basic element in Collective Intelligence experiments. It is important to control this distribution experimentally, asking for criteria that should range from maximum homogeneity to maximum difference. We suggest a method where we obtain these criteria by adding an extra interaction term to the Q-state Potts model, producing a rich vacuum structure. By controlling the two parameters of the model, we can obtain different patterns for the geometrical distribution of the agents. We study the transitions and phase diagram of this model, considering the physics at constant magnetization, and show that the states correspond to a large diversity of mixing patterns, directly applicable to agent distribution in CI experiments.