I don't have any links to studies handy. The
wiki article on LSD mentions risk of psychosis and seems to indicate that supporting data are limited, and that it's not clear whether there's a direct causal connection. Tripping can be an intense, even traumatic experience, so it makes sense intuitively that people with latent disorders might trigger an episode by using psychedelics.
A big part of the problem, IMHO, is how poorly understood 'mental disorders' themselves are, latent or otherwise. In most cases, we classify mental disorders by symptom, and we don't really even know that all cases which are labeled as the same condition have causes that are at all similar. The best we can really do is look at external conditions - drug use, demographics, etc. - and make statistics about how many exhibit certain symptoms.
I could be completely wrong about this, but from what I know of the existing data:
-There's probably a correlation between psychedelic use and psychotic breaks or episodes for people who are prone to have them. This may just be because psychedelics create intense experiences and intense experiences in general trigger episodes, or there may be some other interaction at work.
-There's no evidence that points to psychedelics causing any permanent psychological damage in psychologically healthy people.
One last bit of food for thought: with the right set and setting and a trained guide, psychedelics may very well have a place in *healing* many of these mental disorders. The literature on psychedelic psychotherapy, while quite limited (the government has been very effective at squashing virtually all research in this areas), is very promising, with MDMA and psilocin standing out as excellent therapeutic tools.
Take all of this with a grain of salt, as it really has been a while since I brushed up on the relevant literature.