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摘要翻译：
我们研究了随机场中球形模型的Gibbs态的性质和热力学可观测项。结果表明，在低温临界线上，模型的磁化强度不是自平均的，而是有条件的自平均。我们还表明，当模型过渡到铁磁相时，任意弱的均匀边界场控制随机场的涨落。结果，均匀边界场恢复了热力学观测项的传统自平均，如磁化强度和磁化率。我们还研究了随机场在晶格位产生的有效场，并证明在球形模型的临界温度下，有效场转变为具有长程关联的相。
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英文标题：
《Spherical Model in a Random Field》
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作者：
A.E. Patrick
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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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一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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英文摘要：
We investigate the properties of the Gibbs states and thermodynamic observables of the spherical model in a random field. We show that on the low-temperature critical line the magnetization of the model is not a self-averaging observable, but it self-averages conditionally. We also show that an arbitrarily weak homogeneous boundary field dominates over fluctuations of the random field once the model transits into a ferromagnetic phase. As a result, a homogeneous boundary field restores the conventional self-averaging of thermodynamic observables, like the magnetization and the susceptibility. We also investigate the effective field created at the sites of the lattice by the random field, and show that at the critical temperature of the spherical model the effective field undergoes a transition into a phase with long-range correlations $\sim r^{4-d}$.
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PDF链接：
https://arxiv.org/pdf/709.3579
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