On the local structure of the phase separation line in the two-dimensional Ising system
On the local structure of the phase separation line in the two-dimensional Ising system
复制标题
二维伊辛体系中相分离线的局域结构
DOI：
10.1007/bf01013174
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发表时间：
1981
期刊：
影响因子：
--
通讯作者：
C. Pfister
中科院分区：
文献类型：
--
作者：
J. Bricmont;J. Lebowitz;C. Pfister
我们调查的结构之间的纯相在二维伊辛模型，在格子气语言的液相和气相，在低温下的相分离线。已知这条线的位置波动在热力学极限下发散，这也被认为发生在三维连续液-汽界面上（在没有引力场的情况下）。我们表明，尽管这种全球性的分歧，它是可以精确地定义的相分离线的局部结构。这在低温下有一个有限的、指数小的宽度，它由中心极限定理（1）与适当（发散）长度尺度上的全局涨落的宽度有关。对于临界温度Tc以下的所有温度，后者已经被明确地计算（2），其中它发散为（Tc-T）-1/2。我们还证明了吉布斯公式的表面张力在低温下，它涉及到的相分离线的局部结构。
We investigate the structure of the phase separation line between the pure phases in the two-dimensional Ising model, the liquid and vapor phase in lattice gas language, at low temperatures. The fluctuations in the location of this line are known to diverge in the thermodynamic limit, something which is also believed to happen to the continuum liquid-vapor interface in three dimensions (in the absence of the gravitational field). We show that despite this global divergence it is possible to define precisely the local structure of the phase separation line. This has a finite, exponentially small, width at low temperatures which is related by a central limit theorem(1)to the width of the global fluctuations on the appropriate (divergent) length scale. The latter has been computed explicitly(2)for all temperatures below the critical temperatureTc, where it diverges as (Tc−T)−1/2. We also prove a Gibbs formula for the surface tension at low temperature, which relates it to the local structure of the phase separation line.