- #1
Mikkel
- 27
- 1
- TL;DR Summary
- Simulate 1d percolation. I have to show that the probability of any site belonging to the largest cluster vanishes as N -> infinity
Hello
I am struggeling with a problem, or perhaps more with understanding the problem.
I have to simulate a one dimensional percolation in Python and that part I can do. The issue is understanding the next line of the problem, which I will post here:
"For the largest cluster size S, use finite size scaling, i.e., allow N to increase and plot s ≡ S/N vs. 1/N, to show that the probability of any site to belong to the largest cluster vanishes in the thermodynamic limit. Hint: Use N raised to some power between 2 and 5".
So, the way I understand this is to, let N increase some amount each iteration and find the largest cluster. I save these values and plot S/N vs. 1/N ending up with the attached plot.
I'm just unsure wheter or not this is correctly interpreted and would love to hear others input
Thanks!
I am struggeling with a problem, or perhaps more with understanding the problem.
I have to simulate a one dimensional percolation in Python and that part I can do. The issue is understanding the next line of the problem, which I will post here:
"For the largest cluster size S, use finite size scaling, i.e., allow N to increase and plot s ≡ S/N vs. 1/N, to show that the probability of any site to belong to the largest cluster vanishes in the thermodynamic limit. Hint: Use N raised to some power between 2 and 5".
So, the way I understand this is to, let N increase some amount each iteration and find the largest cluster. I save these values and plot S/N vs. 1/N ending up with the attached plot.
I'm just unsure wheter or not this is correctly interpreted and would love to hear others input
Thanks!