  We investigate the geometry of the critical fluctuations for a general system
undergoing a thermal second order phase transition. Adopting a generalized
effective action for the local description of the fluctuations of the order
parameter at the critical point ($T=T_c$) we show that instanton-like
configurations, corresponding to the minima of the effective action functional,
build up clusters with fractal geometry characterizing locally the critical
fluctuations. The connection between the corresponding (local) fractal
dimension and the critical exponents is derived. Possible extension of the
local geometry of the system to a global picture is also discussed.
