  We propose a new way of investigating phase transitions in the context of
information theory. We use an information-entropic measure of spatial
complexity known as configurational entropy (CE) to quantify both the storage
and exchange of information in a lattice simulation of a Ginzburg-Landau model
with a scalar order parameter coupled to a heat bath. The CE is built from the
Fourier spectrum of fluctuations around the mean-field and reaches a minimum at
criticality. In particular, we investigate the behavior of CE near and at
criticality, exploring the relation between information and the emergence of
ordered domains. We show that as the temperature is increased from below, the
CE displays three essential scaling regimes at different spatial scales: scale
free, turbulent, and critical. Together, they offer an information-entropic
characterization of critical behavior where the storage and processing of
information is maximized at criticality.
