This is tricky. I agree with Interficio that the use of solum together with nihil would most likely make it mean "only nothing happens". I do think nulla res would work better than nihil, since nulla is equivalent to non ulla "not anything." That avoids the meaning "merely nothing happens," making it instead "anything doesn't merely/just happen." It also broadens the meaning of "nothing" a bit.
What I'm less certain about is the word solum itself. Technically, this adverb means "alone" or "on its own," not "merely/just." However, it does make sense to say "not anything [i.e. nothing] happens on its own."
Modo is the basic word for "merely/just", but it also has the temporal sense of "just now", which means it should probably be avoided. To reduce the ambiguity one might use tantummodo "merely just/so much just", a fairly common and well-attested word; but it's also a bit long and looks cumbersome.
Since I can't really decide which of these is best, I'll just give them all and let someone else decide: Nulla res [solum/modo/tantummodo] fit.
