  We investigate the critical behavior of continuous phase transitions in the
context of Ginzburg Landau models with a double well effective potential. In
particular, we show that the recently proposed configurational entropy, a
measure of spatial complexity of the order parameter based on its Fourier mode
decomposition, can be used to identify the critical point. We compute the CE
for different temperatures and show that large spatial fluctuations near the
critical point lead to a sharp decrease in the CE. We further show that the CE
density has a marked scaling behavior near criticality, with the same power law
as Kolmogorov turbulence. We reproduce the behavior of the CE at criticality
with a percolating many bubble model.
