4.7 Article

Percolation on Lieb lattices

期刊

PHYSICAL REVIEW E
卷 104, 期 6, 页码 -

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AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.104.064122

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  1. Brazilian Agency CAPES
  2. Brazilian Agency CNPq
  3. Brazilian Agency FAPERJ

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Researchers studied site and bond percolation on Lieb lattices and used Monte Carlo simulations to obtain accurate critical parameter data. The study found that thresholds increase as the average coordination number decreases, and estimates for the correlation length exponent align with the expectation of no change in the universality class.
We study site- and bond-percolation on a class of lattices referred to as Lieb lattices. In two dimensions the Lieb lattice (LL) is also known as the decorated square lattice, or as the CuO2 lattice; in three dimensions it can be generalized to a layered Lieb lattice or to a perovskite lattice. Emergent electronic phenomena, such as topological states and ferrimagnetism, have been predicted to occur in these systems, which may be realized in optical lattices as well as in solid state. Since the study of the interplay between quantum fluctuations and disorder in these systems requires the availability of accurate estimates of geometrical critical parameters, such as percolation thresholds and correlation length exponents, here we use Monte Carlo simulations to obtain these data for LLs when a site (or bond) is present with probability p. We have found that the thresholds satisfy a mean-field (Bethe lattice) trend, namely that the critical concentration, pc, increases as the average coordination number decreases; our estimates for the correlation length exponent are in line with the expectation that there is no change in the universality class.

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