Question: What are three possible phases for language formation?
Answer: Phase I: $\langle cc \rangle $ increases smoothly for $\wp < 0.4$, indicating that for this domain there is a small correlation between word neighborhoods. Full vocabularies are attained also for $\wp < 0.4$, Phase II: a drastic transition appears at the critical domain $\wp ^* \in (0.4,0.6)$, in which $\langle cc \rangle $ shifts abruptly towards 1. An abrupt change in $V(t_f)$ versus $\wp $ is also found (Fig. FIGREF16) for $\wp ^*$, Phase III: single-word languages dominate for $\wp > 0.6$. The maximum value of $\langle cc \rangle $ indicate that word neighborhoods are completely correlated