Problem 2 – Hint 3

Major hint: consider shape deformation where the topmost step(s) is (are) removed or one or more steps are added.

Be very careful when doing mathematical calculations: many solutions were correctly based on this central idea, but made incorrect assumptions. One of the typical mistakes was assuming that for the new profile, the position of the n-th step is given by x_n=\Delta + \lambda n^{2/3}, with no change in the value of \lambda. The power law x_n \propto n^{2/3} remains definitely to be valid (it has been shown to minimize the energy), but the constant \lambda will change!

When doing your mathematical calculations, you might find it useful to exploit the fact that a small displacement \delta of any of the steps yields the same change \epsilon_n(\delta) in the interaction energy, cf the solution of the EuPhO’s problem.