4 problems

Let $\varphi:\mathbb{Z}^d\to\mathbb{Z}$ be an integer-valued minimal surface in linear disorder, with disorder strength $lambda$. Roughening-transition conjecture. For sufficiently…

Tilted SOS roughening conjecture. The slope should destabilize rigidity and induce Gaussian free field-type behavior of the surface at small $\beta$.

Consider the integer-valued random-field Gaussian free field in dimension $d\ge 5$, with arbitrary temperature and positive disorder strength. A roughening transition is a change b…

The integer-valued random-field Gaussian free field is considered in dimension $d=3$, with temperature and disorder strength as parameters. A roughening transition is a change betw…