基于随机图的铁磁体稀释策略
Dilution of Ferromagnets via a Random Graph-based Strategy
摘要：
铁磁体的动力学和行为具有很大的相关性，甚至超出了统计物理学的领域。在这项工作中，我们提出了一个蒙特卡罗方法，随机图的基础上，建模其稀释。特别是，我们专注于尺寸为$D \ge 4$的铁磁体，它可以近似的居里-外斯模型。由于后者具有作为图形对应物的完整图，因此稀释在这种情况下可以被视为修剪过程。因此，为了利用这种映射，所提出的策略使用Erdens-Renyi图模型的修改版本。在这样做的过程中，我们既能够模拟连续稀释，又能够在一个步骤中实现稀释的铁磁体。通过数值模拟研究了所提出的策略，旨在分析所产生的稀释铁磁体的主要性质和平衡。最后，我们还简要介绍了我们的策略在复杂网络领域的进一步应用。
英文摘要：
The dynamics and behavior of ferromagnets have a great relevance even beyond the domain of statistical physics. In this work, we propose a Monte Carlo method, based on random graphs, for modeling their dilution. In particular, we focus on ferromagnets with dimension $D \ge 4$, which can be approximated by the Curie-Weiss model. Since the latter has as graphic counterpart a complete graph, a dilution can be in this case viewed as a pruning process. Hence, in order to exploit this mapping, the proposed strategy uses a modified version of the Erdős-Renyi graph model. In doing so, we are able both to simulate a continuous dilution, and to realize diluted ferromagnets in one step. The proposed strategy is studied by means of numerical simulations, aimed to analyze main properties and equilibria of the resulting diluted ferromagnets. To conclude, we also provide a brief description of further applications of our strategy in the field of complex networks.
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