小世界网络模型的有效场论。一阶和二阶相变
Effective field theory for models defined over small-world networks. First and second order phase transitions
摘要：
我们提出了一个有效场论的方法来分析，在一个非常一般的方式，模型定义在小世界网络。即使该方法的精确性仅限于顺磁区域和一些特殊的限制，它也提供了精确的临界行为和精确的临界表面和渗滤阈值，从而产生清晰和直接的（也是在计算方面）物理洞察。模型非随机部分的底层结构，即，精确地考虑了填充尺寸为d_0的给定晶格L_0并通过固定耦合J_0相互作用的自旋集合。当J_0 \geq 0时，如已知的，小世界效应引起二阶相变，该相变独立于维度d_0和所添加的随机连通性c而发生。当J_0<0时，出现了一种不同的和新颖的情况，其中除了自旋玻璃化转变之外，还可能发生多个一级和二级相变。作为直接的分析应用，我们分析了Viana-Bray模型（d_0=0），一维链（d_0=1），以及任意d_0的球形模型。
英文摘要：
We present an effective field theory method to analyze, in a very general way, 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 provides, yielding a clear and immediate (also in terms of calculation) physical insight, the exact critical behavior and the exact critical surfaces and percolation thresholds. The underlying structure of the non random part of the model, i.e., the set of spins filling up 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, as is known, to a second-order phase transition that takes place independently of the dimension d_0 and of the added random connectivity c. When J_0<0, a different and novel scenario emerges in which, besides a spin glass transition, multiple first- and second-order phase transitions may take place. As immediate analytical applications we analyze the Viana-Bray model (d_0=0), the one dimensional chain (d_0=1), and the spherical model for arbitrary d_0.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
