Information-Entropic Signature of the Critical Point

We investigate the critical behavior of continuous (second-order) phase transitions in the context of (2+1)-dimensional Ginzburg–Landau models with a double-well effective potential. In particular, we show that the recently-proposed configurational entropy (CE)—a measure of the spatial complexity of the order parameter in momentum space 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 (Tc)—characterized by a divergent correlation length—lead to a sharp decrease in the associated configurational entropy. We further show that the CE density goes from a scale-free to an approximate scaling behavior |k|−5/3 as the critical point is approached. We reproduce the behavior of the CE at criticality with a percolating many-bubble model.