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Percolation on Lieb lattices.

W S Oliveira1, J Pimentel de Lima1, N C Costa2

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Summary
This summary is machine-generated.

This study investigates percolation on Lieb lattices, finding critical concentrations align with mean-field theory as coordination decreases. Correlation length exponents suggest no change in universality class for these lattices.

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Area of Science:

  • Physics
  • Materials Science
  • Statistical Mechanics

Background:

  • Lieb lattices (LLs), including 2D decorated square and 3D perovskite structures, are platforms for emergent phenomena like topological states and ferrimagnetism.
  • These phenomena are relevant to solid-state and optical lattice systems, necessitating accurate geometrical critical parameters for studying disorder and quantum fluctuations.

Purpose of the Study:

  • To determine percolation thresholds and correlation length exponents for site and bond percolation on Lieb lattices.
  • To analyze the behavior of these critical parameters in relation to lattice coordination number and universality classes.

Main Methods:

  • Monte Carlo simulations were employed to estimate percolation thresholds (p_c) and correlation length exponents.
  • The simulations considered site or bond occupation probability 'p' on Lieb lattices.

Main Results:

  • Percolation thresholds on Lieb lattices exhibit a mean-field (Bethe lattice) trend, where p_c increases with decreasing average coordination number.
  • Estimated correlation length exponents are consistent with the absence of a change in the universality class.

Conclusions:

  • The findings provide crucial geometrical critical parameters for Lieb lattice systems.
  • The results support theoretical expectations regarding universality classes in disordered systems on these lattices.