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  • $\begingroup$ Thanks a lot for the detailed answer! I'd have two more questions if that's okay. Concerning your first bullet-point: I understand the random walk argument, but on the other hand I'd imagine that the interaction term favors two neighboring heights to be close to each other, which may be broken by a large enough temperature. So while the interface would do a random walk "to infinity", isn't there still a notion of it going from being smooth to being rough, or does it not make sense to speak about that in such a context? $\endgroup$
    – Wladislaw Krinitsin
    Commented Jul 2 at 19:25
  • $\begingroup$ My other question would be about your last point: as far as I gathered from the literature I found on the topic, the case $h_i \in (-\infty,\infty)$ with a pinning potential would lead to the surface to always be localized at $h=0$. Is that true or is there more to it? $\endgroup$
    – Wladislaw Krinitsin
    Commented Jul 2 at 19:27
  • 2
    $\begingroup$ Yes, it is always localized. But a lot of nontrivial information has been obtained (in particular in the more interesting, higher dimensional case), including in the case where the pinning potential is disordered. $\endgroup$
    – Yvan Velenik
    Commented Jul 2 at 19:49