Interfacial roughening, segregation and dynamic behaviour in a generalized Schelling model

Abstract

The Schelling model is widely used for the study of segregation behaviour in sociodynamics, econophysics, and related disciplines. Agents of two types placed in a lattice or network are allowed to exchange their locations on the basis of a transfer rule (T(S, A)), which depends on the satisfaction that the agent already has in her/his present position (S), and the attractiveness of the future position (A). The satisfaction and the attractiveness that the agent feels are measured in terms of the fraction between the number of agents of the same type that are present in the neighbourhood of the agent under consideration and the total number of neighbours. In this work we propose a generalization of the Schelling model such that the relative influence of satisfaction and attractiveness can be enhanced or depleted by means of an exponent q, i.e. T(S, A) = (1−S)qA. We report extensive Monte Carlo numerical simulations performed for the twodimensional square lattice with initial conditions of two different types: (i) fully disordered configurations of randomly located agents; and (ii) fully segregated configurations with a flat interface between two domains of unlike agents. We show that the proposed model exhibits a rich and interesting complex behaviour that emerges from the competitive interplay between interfacial roughening and the diffusion of isolated agents in the bulk of clusters of unlike agents. The first process dominates the early time regime, while the second one prevails for longer times after a suitable crossover time. Our numerical results are rationalized in terms of a dynamic finite-size scaling ansatz.