Critical phenomena of a hybrid phase transition in cluster merging dynamics

K. Choi, Deokjae Lee, Y. S. Cho, J. C. Thiele, H. J. Herrmann, and B. Kahng
Phys. Rev. E 96, 042148 – Published 24 October 2017

Abstract

Recently, a hybrid percolation transition (HPT) that exhibits both a discontinuous transition and critical behavior at the same transition point has been observed in diverse complex systems. While the HPT induced by avalanche dynamics has been studied extensively, the HPT induced by cluster merging dynamics (HPT-CMD) has received little attention. Here, we aim to develop a theoretical framework for the HPT-CMD. We find that two correlation-length exponents are necessary for characterizing the giant cluster and finite clusters separately. The conventional formula of the fractal dimension in terms of the critical exponents is not valid. Neither the giant nor finite clusters are fractals, but they have fractal boundaries. A finite-size scaling method for the HPT-CMD is also introduced.

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  • Received 19 June 2017
  • Revised 21 August 2017

DOI:https://doi.org/10.1103/PhysRevE.96.042148

©2017 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

K. Choi1, Deokjae Lee1, Y. S. Cho2, J. C. Thiele3, H. J. Herrmann3, and B. Kahng1,*

  • 1CCSS, CTP, and Department of Physics and Astronomy, Seoul National University, Seoul 08826, Korea
  • 2Department of Physics, Chonbuk National University, Jeonju 54896, Korea
  • 3Computational Physics for Engineering Materials, Institute for Building Materials, ETH Zürich, 8093 Zürich, Switzerland

  • *bkahng@snu.ac.kr

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Vol. 96, Iss. 4 — October 2017

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