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arXiv 0705.1406cond-mat.stat-mech
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经典库仑流体数密度关联函数高温极限的一个棘手问题

A Trickiness of the High-Temperature Limit for Number Density Correlation Functions in Classical Coulomb Fluids

L. Samaj

备注：
18 pages, to appear in J. Stat. Phys
发表信息：
J. Stat. Phys. 128 (2007) 569-586
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摘要：

Debye-Hückel理论严格地描述了经典库仑流体在高温$β\to 0$状态（$β$表示逆温度）下的热平衡。一般认为，德拜-休克尔理论和系统的高温膨胀在$β>0$的{ \em严格正}小值区域也提供了充分的描述。本文在二维库仑气体中通过与可积sine-Gordon场模型等价的对数势相互作用的点状$+/-$单位电荷来检验这一假设。特别是，我们应用形状因子的方法来获得粒子关联函数的精确渐近大距离行为，考虑在电荷和数密度组合。我们首先确定的领导和subleading渐近项严格正$β>0$的一般形式，然后评估其高温$β\to 0$形式。在{ \em电荷}关联函数的情况下，在严格正的$β>0$处的领先渐近项也是高温$β\to 0$区域中的领先渐近项。相反，{ \em数密度}关联函数的$β\to 0$行为伴随着前两个渐近项之间的干扰。因此，当从$β>0$的严格正值到德拜-休克尔极限$β\to 0$时，该函数的大距离行为表现出不连续性。这是本文的关键结论：二维库仑气体密度关联函数的大距离渐近性和高温极限不对易。

英文摘要：

The Debye-Hückel theory describes rigorously the thermal equilibrium of classical Coulomb fluids in the high-temperature $β\to 0$ regime ($β$ denotes the inverse temperature). It is generally believed that the Debye-Hückel theory and the systematic high-temperature expansion provide an adequate description also in the region of small {\em strictly positive} values of $β>0$. 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 $β>0$ and then evaluate their high-temperature $β\to 0$ forms. In the case of the {\em charge} correlation function, the leading asymptotic term at a strictly positive $β>0$ is also the leading one in the high-temperature $β\to 0$ regime. On the contrary, the $β\to 0$ 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 $β>0$ to the Debye-Hückel limit $β\to 0$. 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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