  In this paper we extend the results of \cite{S3} to the borderline case $s =
\frac 12$. We obtain the classification of global bounded solutions with
asymptotically flat level sets for semilinear nonlocal equations of the type
$$\Delta^{\frac 12} u=W'(u) \quad \text{in} \quad R^n,$$ where $W$ is a double
well potential.
