The phase transition at , caused by variation of parameters in a lattice dynamic system, is studied by means of classical and quantum-statistical mechanics. We calculate the critical exponents explicitly. They differ from those for . Within the frame of classical statistical mechanics they are nonuniversal, depending on a parameter. This feature is suppressed, however, by quantum fluctuations. The quantum-mechanical critical point for a -dimensional system corresponds to the Wilson fix point of a ()-dimensional system.
- Received 12 February 1976
©1977 American Physical Society