Spin models on random graphs with controlled topologies beyond degree constraints
Spin models on random graphs with controlled topologies beyond degree constraints
复制标题
随机图上的自旋模型具有超出度数限制的受控拓扑
DOI：
10.1088/1751-8113/41/25/255003
复制
发表时间：
2008
期刊：
影响因子：
--
通讯作者：
Acc Coolen
中科院分区：
文献类型：
--
作者：
CJ Pérez Vicente;Acc Coolen
我们研究了有限连接随机相互作用图上的Ising自旋模型，这些图是从一个集合中绘制的，其中不仅可以任意选择度分布p(k)，而且可以通过在所涉及顶点度的任意函数Q（k, k '）的基础上通过优先附加边来进一步微调拓扑。我们利用有限连通性均衡复制理论，在复制对称模型中求解这些模型。在我们的图集合中，发现自旋系统的相图不再仅仅取决于所选择的度分布，而且还取决于所选择的Q（k, k '）。在可解模型中控制相互作用拓扑的能力增加，而不仅仅是规定相互作用图的度分布，这使得在适当定义的随机图上通过自旋系统更准确地建模现实世界的相互作用粒子系统。
We study Ising spin models on finitely connected random interaction graphs which are drawn from an ensemble in which not only the degree distribution p(k) can be chosen arbitrarily, but which allows for further fine tuning of the topology via preferential attachment of edges on the basis of an arbitrary function Q(k, k′) of the degrees of the vertices involved. We solve these models using finite connectivity equilibrium replica theory, within the replica symmetric ansatz. In our ensemble of graphs, phase diagrams of the spin system are found to depend no longer only on the chosen degree distribution, but also on the choice made for Q(k, k′). The increased ability to control interaction topology in solvable models beyond prescribing only the degree distribution of the interaction graph enables a more accurate modeling of real-world interacting particle systems by spin systems on suitably defined random graphs.