Solution Clusters and Monotone-2SAT It is known that generic k-SAT formulas may exhibit the presence of exponentially many solution clusters.

Question:
Is it true also for Monotone-2SAT formulas?

For the definition of cluster, see Kaveh's answer to the question SAT Solution Space - Definition of Cluster of Solutions.
The answer is no.  If you consider a graph with satisfying assignments as vertices where two assignments are joined by an edge if the Hamming distance is 1, the graph is always connected because every satisfying assignment can be eventually transformed to the all-1 assignment by changing the value of one variable from 0 to 1.