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

E. V. ALBANO

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT

IOP PUBLISHING LTD

Lugar: Londres; Año: 2012 vol. 2012 p. 3013 - 3029

1742-5468

in sociodynamics, econophysics, and related disciplines. Agents of twotypes placed in a lattice or network are allowed to exchange their locations onthe basis of a transfer rule (T(S,A)), which depends on the satisfaction that theagent already has in her/his present position (S), and the attractiveness of thefuture position (A). The satisfaction and the attractiveness that the agent feelsare measured in terms of the fraction between the number of agents of the sametype that are present in the neighbourhood of the agent under consideration andthe total number of neighbours. In this work we propose a generalization of theSchelling model such that the relative influence of satisfaction and attractivenesscan 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 twodimensionalsquare lattice with initial conditions of two different types: (i) fullydisordered configurations of randomly located agents; and (ii) fully segregatedconfigurations with a flat interface between two domains of unlike agents. Weshow that the proposed model exhibits a rich and interesting complex behaviourthat emerges from the competitive interplay between interfacial roughening andthe diffusion of isolated agents in the bulk of clusters of unlike agents. The firstprocess dominates the early time regime, while the second one prevails for longertimes after a suitable crossover time. Our numerical results are rationalized interms of a dynamic finite-size scaling ansatz.