小世界网络模型的精确结果和新见解。一阶和二阶相变。I：总体结果
Exact results and new insights for models defined over small-world networks. First and second order phase transitions. I: General result
摘要：
作为一种非常普遍的方法，我们提出了一个有效场论来分析定义在小世界网络上的模型。即使该方法的精确性仅限于顺磁区域和某些特殊的限制，它也给出了精确的临界行为和精确的临界表面和逾渗阈值，并提供了对物理学的清晰和直接（也是在计算方面）的见解。模型的非随机部分的基础结构，即，精确地考虑了停留在维度d_0的给定晶格L_0中并且通过固定耦合J_0相互作用的自旋集合。当J_0 \geq 0时，小世界效应引起已知的事实，即发生二阶相变，与维度d_0和所添加的随机连接性c无关。然而，当J_0<0时，出现了完全不同的情况，其中除了自旋玻璃化转变之外，还可能发生多个一阶和二阶相变。
英文摘要：
We present, as a very general method, an effective field theory to analyze models defined over small-world networks. Even if the exactness of the method is limited to the paramagnetic regions and to some special limits, it gives the exact critical behavior and the exact critical surfaces and percolation thresholds, and provide a clear and immediate (also in terms of calculation) insight of the physics. The underlying structure of the non random part of the model, i.e., the set of spins staying in a given lattice L_0 of dimension d_0 and interacting through a fixed coupling J_0, is exactly taken into account. When J_0\geq 0, the small-world effect gives rise to the known fact that a second order phase transition takes place, independently of the dimension d_0 and of the added random connectivity c. However, when J_0<0, a completely different scenario emerges where, besides a spin glass transition, multiple first- and second-order phase transitions may take place.
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