  The basic notion of percolation in physics assumes the emergence of a giant
connected (percolation) cluster in a large disordered system when the density
of connections exceeds some critical value. Until recently, the percolation
phase transitions were believed to be continuous, however, in 2009, a
remarkably different, discontinuous phase transition was reported in a new
so-called "explosive percolation" problem. Each link in this problem is
established by a specific optimization process. Here, employing strict
analytical arguments and numerical calculations, we find that in fact the
"explosive percolation" transition is continuous though with an uniquely small
critical exponent of the percolation cluster size. These transitions provide a
new class of critical phenomena in irreversible systems and processes.
