摘要翻译：
我们将著名的Peierls的论点推广到研究长程相互作用经典固体的稳定性。长程相互作用意味着所有的原子振子通过一个谐波势相互耦合，尽管耦合强度以幂律形式衰减，其中$x$是振子之间的距离。我们发现，对于程参数$α<2$,长程相互作用占主导地位，即使在有限温度下，一维系统仍保持晶序；而对于$αGeq2$,即使在极小温度下，长程晶序也消失。我们还研究了在t=0时量子涨落对一维固体熔化行为的影响，将Peierls的论点推广到量子振子的情况。
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英文标题：
《The effect of long range interactions on the stability of classical and
  quantum solids》
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作者：
Debanjan Chowdhury and Amit Dutta
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最新提交年份：
2008
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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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英文摘要：
  We generalise the celebrated Peierls' argument to study the stability of a long-range interacting classical solid. Long-range interaction implies that all the atomic oscillators are coupled to each other via a harmonic potential, though the coupling strength decays as a power-law $1/x^{\alpha}$, where $x$ is the distance between the oscillators. We show that for the range parameter $\alpha <2$, the long-range interaction dominates and the one-dimensional system retains a crystalline order even at a finite temperature whereas for $\alpha \geq2$, the long-range crystalline order vanishes even at an infinitesimally small temperature. We also study the effect of quantum fluctuations on the melting behaviour of a one-dimensional solid at T=0, extending Peierls' arguments to the case of quantum oscillators.
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PDF链接：
https://arxiv.org/pdf/801.0299