Colored percolation

Sumanta Kundu and S. S. Manna
Phys. Rev. E 95, 052124 – Published 15 May 2017

Abstract

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 (1q)/(nm). 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.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
5 More
  • Received 28 February 2017

DOI:https://doi.org/10.1103/PhysRevE.95.052124

©2017 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Sumanta Kundu and S. S. Manna

  • Satyendra Nath Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata-700106, India

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 95, Iss. 5 — May 2017

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×