Does the binomial random graph model $G(n, (\ln n)/n^2)$ obey zero-one law?

Question

I want to know if the bionomial random graph model $G\left(n, \frac{\ln n}{n^2}\right)$ obeys Zero-one law or not?

I know that $\frac{\ln n}{n}$ is a threshold function for connectivity and for $\frac{\ln n}{n}$ zero-one law doesn't hold but what's about $\frac{\ln n}{n^2}$?