  We show that the spontaneous symmetry breaking can be defined also for finite
systems based on the properly defined jump probability between the ground
states in the 2d and 3d Ising models on a square and a cubic lattice
respectively. Our analysis reveals the existence of an interval in the
temperature (control parameter) space within which the spontaneous symmetry
breaking takes place. The upper limit of this region is the pseudocritical
point where the symmetric vacuum bifurcates in energetically degenerate
non-symmetric vacua, initiating the spontaneous symmetry breaking process. The
lower limit, identified as the temperature value at which the spontaneous
symmetry breaking is completed, is characterized by maximal characteristic time
for the decay of magnetization (order parameter) auto-correlations. We argue
that this anomalous enhancement of auto-correlations is attributed to the
transition from type I to on-off intermittency in the order parameter dynamics.
Possible phenomenological implications of this behaviour are briefly discussed.
