Python – a Tool for Percolation Analysis in Triangular Lattice

Authors N. Gupta1, M. Nath1, S. Chakraborty2 , A. Bandyopadhyay3

1Department of Physics, Lovely Professional University, Phagwara 144411, Punjab, India

2Jagannath Kishore College, P.O. Purulia, Dist. Purulia, West Bengal 723101, India

3Department of Physics, University of Gour Banga, NH-34, P.O. Mokdumpur, Dist. Malda, West Bengal, India

Issue Volume 13, Year 2021, Number 2
Dates Received 11 January 2021; revised manuscript received 28 March 2021; published online 09 April 2021
Citation N. Gupta, M. Nath, S. Chakraborty, A. Bandyopadhyay, J. Nano- Electron. Phys. 13 No 2, 02009 (2021)
PACS Number(s) 64.60.ah, 05.10.Ln
Keywords Percolation threshold, Monte-Carlo simulation, HK algorithm.

Percolation theory, developed more than 60 years before to describe the behavior of flow phenomena in porous medium, has undergone an extensive area of applications in recent years, ranging from epidemiology, financial market, soil science, pharmaceutical technology to composite material structure. Here in this paper, percolation theory is applied to the triangular lattice and its characterization has been done using Monte-Carlo simulation. Python language has been used to develop the code. For this, we have used the inbuilt libraries of Python like NumPy, SciPy, Matplotlib etc. Hoshen-Kopelman (HK) algorithm is used to identify the cluster and its numbering procedure. This algorithm is being preferred over the other methods as it consumes low computer memory and less computation time. The prime point of interest in percolation is known as percolation threshold (pc) which is computed for our case is 0.5. We have also characterized the percolation by finding the other quantities as: normalized mass of cluster (M), percolation probability (Pp), the density of the infinite cluster (P∞) and ordered parameter Ω(L). We have extracted critical exponents from our data and found that they match exactly with their universal values. To the best of our knowledge, we are the first group to report percolation in triangular lattice by means of HK algorithm using Python language.

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