Information-Entropic Signature of the Critical Point

TL;DR

This paper demonstrates that configurational entropy, derived from Fourier modes of the order parameter, effectively identifies the critical point in phase transitions and exhibits scaling behavior similar to turbulence.

Contribution

It introduces the use of configurational entropy to detect critical points and analyzes its scaling behavior near criticality in Ginzburg Landau models.

Findings

CE sharply decreases near the critical point

CE density follows a power-law scaling at criticality

Percolating bubble model reproduces CE behavior at criticality

Abstract

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.