Profile and width of rough interfaces

TL;DR

This paper investigates the separation of intrinsic interface profiles from capillary wave fluctuations in the 3D Ising model, confirming capillary wave theory at large scales but not observing an intrinsic regime.

Contribution

It introduces a blocking procedure and a new method for analyzing interface profiles, challenging the expectation of observing an intrinsic regime.

Findings

Capillary wave theory is validated at large length scales.

No intrinsic interface regime is observed in the simulations.

A novel method for interface position determination is proposed.

Abstract

In the context of Landau theory and its field theoretical refinements, interfaces between coexisting phases are described by intrinsic profiles. These intrinsic interface profiles, however, are neither directly accessible by experiment nor by computer simulation as they are broadened by long-wavelength capillary waves. In this paper we study the separation of the small scale intrinsic structure from the large scale capillary wave fluctuations in the Monte Carlo simulated three-dimensional Ising model. To this purpose, a blocking procedure is applied, using the block size as a variable cutoff, and a translationally invariant method to determine the interface position of strongly fluctuating profiles on small length scales is introduced. While the capillary wave picture is confirmed on large length scales and its limit of validity is estimated, an intrinsic regime is, contrary to expectations, not observed.