  The second moment method has always been an effective tool to lower bound the
satisfiability threshold of many random constraint satisfaction problems.
However, the calculation is usually hard to carry out and as a result, only
some loose results can be obtained. In this paper, based on a delicate analysis
which fully exploit the power of the second moment method, we prove that random
RB instances can exhibit exact phase transition under more relaxed conditions,
especially slower-growing domain size. These results are the best by using the
second moment method, and new tools should be introduced for any better
results.
