There are two events specifically in this chapter that could contain an element of mystical power.
First, Simon disappears from the rest of the group. Usually the little ones can find him. People seem to always have Simon near when they need something, but in the middle of this chapter he just took off to be by himself after his idea was rejected. No one noticed at first, but after awhile Ralph and Piggy notice.
The second event that is probably the one you need occurs when Simon spends moments with the Lord of the Flies. Simon is not necessarily the one in control of this power, in fact, it feels as if it is inflicted upon him. This dead pig's head put on a stick seems to be talking with him. He feels the pig call him a silly boy and taunt him, although we know that what is occurring is not real.
“Fancy thinking the Beast was something you could hunt and kill!” said the head. For a moment or two the forest and all the other dimly appreciated places echoed with the parody of laughter.
“You knew, didn’t you? I’m part of you? Close, close, close! I’m the reason why it’s no go? Why things are what they are?” The laughter shivered again.
“Come now,” said the Lord of the Flies. “Get back to the others and we’ll forget the whole thing.”
Simon inserted his head into the mouth of the Lord of the Flies and we understand that he comprehended how evil is a part of all. The Beast lives within all of us. Simon lost consciousness. This was a vivid hallucination for a boy of his age.