摘要翻译：
我们研究了小世界超图上带有键无序的自旋系统的热力学性质，该超图是将一维Ising链叠加到带有p-自旋相互作用的随机Bethe图上得到的。利用转移矩阵技术，我们分别在复制对称和一步复制对称破缺近似下，导出了描述相关序参量和自由能的不动点方程。我们确定了所有温度下复制品对称性内的静态和动态铁磁相变以及spinglass相变，并证明了当考虑到复制品对称性一步破缺时对这些结果的修正。所得结果与Monte-Carlo模拟结果一致。
---
英文标题：
《Small-world hypergraphs on a bond-disordered Bethe lattice》
---
作者：
D. Boll\'e, R. Heylen
---
最新提交年份：
2007
---
分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
--
一级分类：Physics        物理学
二级分类：Disordered Systems and Neural Networks        无序系统与神经网络
分类描述：Glasses and spin glasses; properties of random, aperiodic and quasiperiodic systems; transport in disordered media; localization; phenomena mediated by defects and disorder; neural networks
眼镜和旋转眼镜；随机、非周期和准周期系统的性质；无序介质中的传输；本地化；由缺陷和无序介导的现象；神经网络
--

---
英文摘要：
  We study the thermodynamic properties of spin systems with bond-disorder on small-world hypergraphs, obtained by superimposing a one-dimensional Ising chain onto a random Bethe graph with p-spin interactions. Using transfer-matrix techniques, we derive fixed-point equations describing the relevant order parameters and the free energy, both in the replica symmetric and one step replica symmetry breaking approximation. We determine the static and dynamic ferromagnetic transition and the spinglass transition within replica symmetry for all temperatures, and demonstrate corrections to these results when one step replica symmetry breaking is taken into account. The results obtained are in agreement with Monte-Carlo simulations.
---
PDF链接：
https://arxiv.org/pdf/711.3757