Dynamic renormalization group study of a generalized continuum model of crystalline surfaces.
Dynamic renormalization group study of a generalized continuum model of crystalline surfaces.
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DOI：
10.1103/physreve.65.016110
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发表时间：
2001-10
期刊：
影响因子：
--
通讯作者：
R. Cuerno;E. Moro
中科院分区：
文献类型：
--
作者：
R. Cuerno;E. Moro
我们将诺齐埃尔斯 - 加莱动态重整化群（RG）方案应用于一个d维表面的连续平衡模型，该表面通过线性表面张力和线性表面扩散弛豫，并且受到一个有利于高度变量离散值的晶格势的作用。因此，该模型在过阻尼正弦 - 戈登模型和一个相关的无张力晶体表面的连续模型之间进行插值。RG流预测仅在d = 2维表面存在平衡粗糙化转变，处于爱德华兹 - 威尔金森（EW）普适类中的低温平坦相和高温粗糙相之间。对于任何其他基底维度d>2，表面总是处于平坦相。对于任何d值，线性表面扩散机制是对线性表面张力机制的一种无关扰动，但可能会引起长时间的交叉，在其中可以观察到线性分子束外延方程的标度性质，从而提高正弦 - 戈登粗糙化温度的值。这种现象源于非线性晶格势，并且即使在没有裸表面张力项的情况下也会发生。这的一个重要结果是，无张力晶体表面在高温下渐近地由EW普适类描述。
We apply the Nozières-Gallet dynamic renormalization group (RG) scheme to a continuum equilibrium model of a d-dimensional surface relaxing by linear surface tension and linear surface diffusion, and which is subject to a lattice potential favoring discrete values of the height variable. The model thus interpolates between the overdamped sine-Gordon model and a related continuum model of crystalline tensionless surfaces. The RG flow predicts the existence of an equilibrium roughening transition only for d=2 dimensional surfaces, between a flat low-temperature phase and a rough high-temperature phase in the Edwards-Wilkinson (EW) universality class. The surface is always in the flat phase for any other substrate dimensions d>2. For any value of d, the linear surface diffusion mechanism is an irrelevant perturbation of the linear surface tension mechanism, but may induce long crossovers within which the scaling properties of the linear molecular-beam epitaxy equation are observed, thus increasing the value of the sine-Gordon roughening temperature. This phenomenon originates in the nonlinear lattice potential, and is seen to occur even in the absence of a bare surface tension term. An important consequence of this is that a crystalline tensionless surface is asymptotically described at high temperatures by the EW universality class.