In that work, the effect of next-nearest-neighbor (NNN) interactions $\epsilon_2$ was crudely estimated by examining a general formula obtained by Akutsu and Akutsu,[@AA] showing a correction of order $\exp(-\epsilon_2/k_BT)$, which was glibly deemed to be insignificant. In subsequent work the Twente group [@ZP1] considered steps in just the two principal directions and showed that if one included an attractive NNN interaction, one could evaluate the step free energies and obtain a ratio consistent with the experimental results in Ref. . This group later extended their calculations[@ZP2] to examine the stiffness.

To make contact with experiment, one typically first gauges the diffusivity along a close-packed direction and from it extracts the ratio of the elementary kink energy $\varepsilon_k$ to $T$. Arguably the least ambiguous way to relate $\varepsilon_k$ to bonds in a lattice gas model is to extract an atom from the edge and place it alongside the step well away from the new unit indentation, thereby creating four kinks.[@nelson] The removal of the step atom costs energy $3\epsilon_1\! +\! 2\epsilon_2$ while its replacement next to the step recoups $\epsilon_1\! +\! 2\epsilon_2$. Thus, whether or not there are NNN interactions, we identify $\varepsilon_k \! =\! -\scriptstyle{\frac{1}{2}}\textstyle\epsilon_1 \! =\! \scriptstyle{\frac{1}{2}}\textstyle|\epsilon_1|$ (since the 