Roughening of interfaces implies the divergence of the interface width w with the system size L. For two-dimensional systems the divergence of \(w^2\) is linear in L. In the framework of a detailed capillary wave approximation and of statistical field theory we derive an expression for the asymptotic behaviour of \(w^2\), which differs from results in the literature. It is confirmed by Monte Carlo simulations.

中文翻译：

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二维界面粗糙化

接口的粗糙化意味着接口宽度w与系统大小L的差异。对于二维系统，\（w ^ 2 \）的散度在L中是线性的。在详细的毛细管波逼近和统计场论的框架下，我们推导了\（w ^ 2 \）渐近行为的表达式，该表达式与文献中的结果有所不同。蒙特卡洛模拟证实了这一点。