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摘要翻译：
我们定义了一个新的随机自旋模型族，它具有一维结构、有限范围的多自旋相互作用和有界的平均度（每个自旋参与的相互作用的数目）。非受挫基态可以描述为一个稀疏的带对角线性系统的解，从而允许有效的数值分析。在无限大的相互作用范围内，我们恢复了所谓的稀释p自旋模型，即随着平均度的增加，会发生一个随机的一级相变。在这里，我们研究一个大而有限的相互作用范围的最重要的后果：(i)涨落引起的热力学量的修正；(ii)需要一个非均匀的（与位置相关的）序参量；(iii)有限镶嵌长度尺度的出现。特别地，我们研究了平均场玻璃化转变时的相关长度发散。
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英文标题：
《A simple one dimensional glassy Kac model》
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作者：
Andrea Montanari and Antoine Sinton
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最新提交年份：
2007
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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
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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
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英文摘要：
We define a new family of random spin models with one-dimensional structure, finite-range multi-spin interactions, and bounded average degree (number of interactions in which each spin participates). Unfrustrated ground states can be described as solutions of a sparse, band diagonal linear system, thus allowing for efficient numerical analysis. In the limit of infinite interaction range, we recover the so-called XORSAT (diluted p-spin) model, that is known to undergo a random first order phase transition as the average degree is increased. Here we investigate the most important consequences of a large but finite interaction range: (i) Fluctuation-induced corrections to thermodynamic quantities; (ii) The need of an inhomogeneous (position dependent) order parameter; (iii) The emergence of a finite mosaic length scale. In particular, we study the correlation length divergence at the (mean-field) glass transition.
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PDF链接：
https://arxiv.org/pdf/705.0054
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