摘要翻译：
我们用大数定律计算了无序urn模型的自由能。结果表明，用大数定律得到的鞍点方程与用复制法得到的鞍点方程是相同的。因此，我们得出结论，对于无序的urn模型，复制对称解是足够的。此外，我们还指出了urn模型与随机场Ising模型自由能的数学相似性；这种相似性证明了urn模型的复制对称解是精确的。
---
英文标题：
《Free energy of disordered urn models in the canonical ensemble》
---
作者：
Jun Ohkubo
---
最新提交年份：
2007
---
分类信息：

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
--
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
--

---
英文摘要：
  We calculate the free energy of the disordered urn model using the law of large numbers. It is revealed that the saddle point equation obtained by the usage of the law of large numbers is the same as that obtained by the replica method. Hence, we conclude that the replica symmetric solution is adequate for the disordered urn model. Furthermore, we point out the mathematical similarity of free energies between the urn models and the Random Field Ising Model; this similarity gives an evidence that the replica symmetric solution of the urn models is exact.
---
PDF链接：
https://arxiv.org/pdf/705.2104