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Investigating nonrandom percolation models, this study reveals that removing randomness fundamentally alters critical behavior. The fractal dimensions and critical exponents differ significantly from random percolation, suggesting new universality classes.

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Area of Science:

  • Statistical physics
  • Complex systems
  • Condensed matter physics

Background:

  • Percolation theory describes the formation of connected clusters.
  • Quenched randomness is a key feature of many real-world systems.
  • Understanding critical phenomena in nonrandom systems is crucial for theoretical advancements.

Purpose of the Study:

  • To investigate the behavior of the percolation transition without quenched randomness.
  • To explore nonrandom self-dual quasiperiodic models on a square lattice.
  • To compare critical properties with those of random percolation.

Main Methods:

  • Studied two nonrandom self-dual quasiperiodic bond percolation models.
  • Analyzed emergent discrete scale invariance at the critical point.
  • Numerically determined fractal dimensions and critical exponents using cluster sizes and wrapping probabilities on a torus.

Main Results:

  • Identified emergent discrete scale invariance but not conformal symmetry.
  • Calculated fractal dimensions (D_f) of 1.911943(1) and 1.707234(40), differing from random percolation (1.89583...).
  • Found critical exponents (ν) well below the random percolation value of 4/3.

Conclusions:

  • The absence of randomness fundamentally changes critical percolation behavior.
  • These nonrandom models may not belong to established universality classes.
  • The findings highlight the significant impact of randomness on critical phenomena.