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摘要翻译：
Debye-H\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\本文在二维库仑气体中证明了这一假设，这种库仑气体中的点状单位电荷通过对数势相互作用，而对数势等效于一个可积的sine-Gordon场模型。特别地，我们应用形状因子方法得到了考虑电荷和数密度组合的粒子关联函数的精确渐近大距离行为。我们首先确定了严格正$\beta>0$时导项和次导项的一般形式，然后求出了它们的高温$\beta\-0$形式。对于{em电荷}关联函数，在严格为正的$\beta>0$处的领先渐近项也是在高温$\beta\to0$区域的领先渐近项。相反，{em数密度}相关函数的$\beta\to0$行为伴随着前两个渐近项之间的干涉。结果表明，该函数的大距离行为在从严格的正值$β>0$到
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英文标题：
《A Trickiness of the High-Temperature Limit for Number Density
Correlation Functions in Classical Coulomb Fluids》
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作者：
L. Samaj
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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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英文摘要：
The Debye-H\"uckel theory describes rigorously the thermal equilibrium of classical Coulomb fluids in the high-temperature $\beta\to 0$ regime ($\beta$ denotes the inverse temperature). It is generally believed that the Debye-H\"uckel theory and the systematic high-temperature expansion provide an adequate description also in the region of small {\em strictly positive} values of $\beta>0$. This hypothesis is tested in the present paper on a two-dimensional Coulomb gas of pointlike $+/-$ unit charges interacting via a logarithmic potential which is equivalent to an integrable sine-Gordon field model. In particular, we apply a form factor method to obtain the exact asymptotic large-distance behavior of particle correlation functions, considered in the charge and number density combinations. We first determine the general forms of the leading and subleading asymptotic terms at strictly positive $\beta>0$ and then evaluate their high-temperature $\beta\to 0$ forms. In the case of the {\em charge} correlation function, the leading asymptotic term at a strictly positive $\beta>0$ is also the leading one in the high-temperature $\beta\to 0$ regime. On the contrary, the $\beta\to 0$ behavior of the {\em number density} correlation function is accompanied by an interference between the first two asymptotic terms. Consequently, the large-distance behavior of this function exhibits a discontinuity when going from strictly positive values of $\beta>0$ to the Debye-H\"uckel limit $\beta\to 0$. This is the crucial conclusion of the paper: the large-distance asymptotics and the high-temperature limit do not commute for the density correlation function of the two-dimensional Coulomb gas.
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PDF链接：
https://arxiv.org/pdf/705.1406
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