基于地理学的区域发展：一种统计力学方法
Territorial Developments Based on Graffiti: a Statistical Mechanics Approach
摘要：
我们研究了著名的帮派聚集和领土形成的社会学现象，通过一个相互作用的代理系统定义在一个格子。我们引入了一个两帮哈密顿模型，代理人有红色或蓝色的联系，但在其他方面无法区分。在这个模型中，所有的相互作用都是间接的，只通过涂鸦标记发生，现场以及最近的邻居位置。我们还允许帮派扩散和涂鸦镇压。在这个模型的背景下，我们表明，帮派集群和领土的形成可能会出现在特定的参数选择和相变之间可能会发生混合良好，可能稀释配置和良好分离，集群的。利用统计力学的方法，我们研究了这两种性质不同的情况之间的相变。在这个模型的平均场再现，我们确定参数制度的过渡是第一或第二阶。在所有情况下，我们已经发现，过渡是一个后果完全的帮派涂鸦耦合，这意味着直接帮派帮派的相互作用是不是严格必要的帮派领土的形成，特别是，涂鸦可能是唯一的驱动力背后的帮派集群。我们进一步讨论可能的社会学-以及生态-我们的结果的后果。
英文摘要：
We study the well-known sociological phenomenon of gang aggregation and territory formation through an interacting agent system defined on a lattice. We introduce a two-gang Hamiltonian model where agents have red or blue affiliation but are otherwise indistinguishable. In this model, all interactions are indirect and occur only via graffiti markings, on-site as well as on nearest neighbor locations. We also allow for gang proliferation and graffiti suppression. Within the context of this model, we show that gang clustering and territory formation may arise under specific parameter choices and that a phase transition may occur between well-mixed, possibly dilute configurations and well separated, clustered ones. Using methods from statistical mechanics, we study the phase transition between these two qualitatively different scenarios. In the mean-field rendition of this model, we identify parameter regimes where the transition is first or second order. In all cases, we have found that the transitions are a consequence solely of the gang to graffiti couplings, implying that direct gang to gang interactions are not strictly necessary for gang territory formation; in particular, graffiti may be the sole driving force behind gang clustering. We further discuss possible sociological -- as well as ecological -- ramifications of our results.
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