Gauvin Laetitia, Nadal Jean-Pierre, Vannimenus Jean
Laboratoire de Physique Statistique (LPS), UMR 8550 CNRS, ENS, UPMC Univ. Paris 6 and Univ. Paris Diderot Paris 7-Ecole Normale Supérieure, Paris, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Jun;81(6 Pt 2):066120. doi: 10.1103/PhysRevE.81.066120. Epub 2010 Jun 25.
In the 70s Schelling introduced a multiagent model to describe the segregation dynamics that may occur with individuals having only weak preferences for "similar" neighbors. Recently variants of this model have been discussed, in particular, with emphasis on the links with statistical physics models. Whereas these models consider a fixed number of agents moving on a lattice, here, we present a version allowing for exchanges with an external reservoir of agents. The density of agents is controlled by a parameter which can be viewed as measuring the attractiveness of the city lattice. This model is directly related to the zero-temperature dynamics of the Blume-Emery-Griffiths spin-1 model, with kinetic constraints. With a varying vacancy density, the dynamics with agents making deterministic decisions leads to a variety of "phases" whose main features are the characteristics of the interfaces between clusters of agents of different types. The domains of existence of each type of interface are obtained analytically as well as numerically. These interfaces may completely isolate the agents leading to another type of segregation as compared to what is observed in the original Schelling model, and we discuss its possible socioeconomic correlates.
20世纪70年代，谢林引入了一个多主体模型来描述隔离动态，这种动态可能发生在个体对“相似”邻居只有微弱偏好的情况下。最近，人们讨论了该模型的变体，特别是强调了与统计物理模型的联系。这些模型考虑的是在晶格上移动的固定数量的主体，而在这里，我们提出了一个允许与外部主体库进行交换的版本。主体的密度由一个参数控制，该参数可以被视为衡量城市晶格的吸引力。这个模型与具有动力学约束的布卢姆-埃默里-格里菲斯自旋-1模型的零温度动力学直接相关。随着空位密度的变化，主体做出确定性决策的动力学导致了各种“相”，其主要特征是不同类型主体簇之间界面的特性。通过解析和数值方法都得到了每种类型界面的存在域。与原始谢林模型中观察到的情况相比，这些界面可能会完全隔离主体，从而导致另一种类型的隔离，并且我们讨论了其可能的社会经济关联。
