  Macroscopic systems often display phase transitions where certain physical
quantities are singular or self-similar at different (spatial) scales. Such
properties of systems are currently characterized by some order parameters and
a few critical exponents. Nevertheless, recent studies show that the
multifractality, where a large number of exponents are needed to quantify
systems, appears in many complex systems displaying self-similarity. Here we
propose a general approach and show that the appearance of the multifractality
of an order parameter related quantity is the signature of a physical system
transiting from one phase to another. The distribution of this quantity
obtained within suitable (time) scales satisfies a $q$-Gaussian distribution
plus a possible Cauchy distributed background. At the critical point the
$q$-Gaussian shifts between Gaussian type with narrow tails and
L$\acute{\text{e}}$vy type with fat tails. Our results suggest that the Tsallis
$q$-statistics, besides the conventional Boltzmann-Gibbs statistics, may play
an important role during phase transitions.
