Abstract
The Schelling model is widely used for the study of segregation behaviour insociodynamics, econophysics, and related disciplines. Agents of two types placed in a latticeor 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 thefraction between the number of agents of the same type that are present in the neighbourhoodof the agent under consideration and the total number of neighbours. In this work wepropose a generalization of the Schelling model such that the relative influence ofsatisfaction and attractiveness can be enhanced or depleted by means of an exponentq, i.e. T(S, A) = (1 − S)qA.We report extensive Monte Carlo numerical simulations performed for the two-dimensionalsquare lattice with initial conditions of two different types: (i) fully disorderedconfigurations of randomly located agents; and (ii) fully segregated configurations with aflat interface between two domains of unlike agents. We show that the proposed modelexhibits a rich and interesting complex behaviour that emerges from the competitiveinterplay between interfacial roughening and the diffusion of isolated agents in the bulkof 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 scalingansatz.
Published Version
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