Random-fractal Ansatz for the configurations of two-dimensional critical systems

Ching Hua Lee, Dai Ozaki, Hiroaki Matsueda

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


Critical systems have always intrigued physicists and precipitated the development of new techniques. Recently, there has been renewed interest in the information contained in the configurations of classical critical systems, whose computation do not require full knowledge of the wave function. Inspired by holographic duality, we investigated the entanglement properties of the classical configurations (snapshots) of the Potts model by introducing an Ansatz ensemble of random fractal images. By virtue of the central limit theorem, our Ansatz accurately reproduces the entanglement spectra of actual Potts snapshots without any fine tuning of parameters or artificial restrictions on ensemble choice. It provides a microscopic interpretation of the results of previous studies, which established a relation between the scaling behavior of snapshot entropy and the critical exponent. More importantly, it elucidates the role of ensemble disorder in restoring conformal invariance, an aspect previously ignored. Away from criticality, the breakdown of scale invariance leads to a renormalization of the parameter Σ in the random fractal Ansatz, whose variation can be used as an alternative determination of the critical exponent. We conclude by providing a recipe for the explicit construction of fractal unit cells consistent with a given scaling exponent.

Original languageEnglish
Article number062144
JournalPhysical Review E
Issue number6
Publication statusPublished - 2016 Dec 28
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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