Yes. Schizophrenia is caused by a malfunction of the brain; therefore, it is an organic mental disorder.

An organic mental disorder or organic mental illness is one that is caused by bodily disease. For instance, syphilitic insanity is an organic mental disorder.

An organic mental disorder is a dysfunction of the brain that may be permanent or temporary.

Anorexia nervosa is indeed a mental disorder.

Organic Mental Health problems have an identifiable physical cause; such as in the dementias or some people with brain injury.

Functional Mental Health Problems are not due to simple structural abnormalities of the brain. There is no 100% identifiable cause for these illnesses. The jury is still out.