Abstract
Percolation refers to the emergence of a giant connected cluster in a
disordered system when the number of connections between nodes exceeds a
critical value. The percolation phase transitions were believed to be
continuous until recently when in a new so-called "explosive percolation"
problem for a competition driven process, a discontinuous phase transition was
reported. The analysis of evolution equations for this process showed however
that this transition is actually continuous though with surprisingly tiny
critical exponents. For a wide class of representative models, we develop a
strict scaling theory of this exotic transition which provides the full set of
scaling functions and critical exponents. This theory indicates the relevant
order parameter and susceptibility for the problem, and explains the continuous
nature of this transition and its unusual properties.
Users
Please
log in to take part in the discussion (add own reviews or comments).