  Phase transition and critical phenomenon is a very interesting topic in
thermodynamics and statistical mechanics. Gravity is believed to has deep and
inherent relation to thermodynamics. Near the critical point, the perturbation
becomes significant. Thus for ordinary matter (govern by interactions besides
gravity) the critical behavior will become very different if we ignore the
perturbations around the critical point, such as mean field theory. We find
that the critical exponents for RN-AdS spacetime keeps the same values even we
consider the full quantum perturbations. This indicates a key difference
between gravity and ordinary thermodynamic system.
