2017/05/15 by Sumanta Kundu, S. S. Manna · 7 citations
Mathematics · Physics and Astronomy · #Alphabet #Colored #Combinatorics #Lattice (music) #Limiting #Mathematics #Physics #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.95.052124
published in Physical review. E 95(5), 052124 (American Physical Society)
openalex publication_date 2017/05/15 · arxiv created 2017/09/04 · arxiv updated 2017/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A model called "colored percolation" has been introduced with its infinite number of versions in two dimensions. The sites of a regular lattice are randomly occupied with probability p and are then colored by one of the n distinct colors using uniform probability q=1/n. Denoting different colors by the letters of the Roman alphabet, we have studied different versions of the model like AB,ABC,ABCD,ABCDE,... etc. Here, only those lattice bonds having two different colored atoms at the ends are defined as connected. The percolation threshold pc(n) asymptotically converges to its limiting value of pc as 1/n. The model has been generalized by introducing a preference towards a subset of colors when m out of n colors are selected with probability q/m each and the rest of the colors are selected with probability (1-q)/(n-m). It has been observed that pc(q,m) depends nontrivially on q and has a minimum at qmin=m/n. In another generalization the fractions of bonds between similarly and dissimilarly colored atoms have been treated as independent parameters. Phase diagrams in this parameter space have been drawn exhibiting percolating and nonpercolating phases.