Abstract
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.
Highlights
Roughening of interfaces in three-dimensional thermodynamical systems is a well-studied phenomenon [1,2,3,4,5,6,7]
2 Theoretical Results for the Interface Width. In view of these conflicting results we shall investigate the divergence of the interface width with the system size L more thoroughly
In the capillary wave approximation the interface is in the scaling region near the critical point represented by a continuous line, whose transverse elongation h(x) (“height”) is Gaussian distributed with a probability distribution pCWA ∝ exp
Summary
Roughening of interfaces in three-dimensional thermodynamical systems is a well-studied phenomenon [1,2,3,4,5,6,7]. In a range of temperatures TR < T < Tc below the critical point, the corresponding breaking of translation invariance is associated with Goldstone modes, which manifest themselves as long-wavelength fluctuations of the interface and lead to its roughening. The most characteristic feature of interface roughening is the fact that the width of the interface increases with the size of the system. In the so-called capillary wave approximation [1,3] the width w of an interface with quadratic shape L × L is given by an integral over wave numbers q w2. The lower cutoff on wave numbers is given by qmin = 2π/L. The upper cutoff represents the scale beyond which the capillary.
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