Week 3

Question 1

What is the idea of percolation?

Answer 1

Question 2

Give a simple example of a usage of percolation, where you have a square lattice, where you’d like to want to get the maximum size of the largest group.
What is the Intensive parameter? What is the order parameter?

Answer 2

Question 3

For site percolation in 1D, what do N(s, p), n(s,p), sn(s, p) and n(s, p) mean?

Answer 3

Question 4

What is an Intensive parameter?

Answer 4

Question 5

How can n(s, p) be rewritten?

Answer 5

Question 6

What is the critical component sigma? What does it represent? What is it for 1D percolation?

Answer 6

Question 7

What is the probability that a site belongs to any cluster? (1D percolation)

Answer 7

Question 8

What is the probability that a site of size s belongs to a cluster?

Answer 8

Question 9

What is the mean cluster size? How is it derived?

Answer 9

Question 10

What is the critical component gamma? How is it related to percolation?

Answer 10

Question 11

What is the correlation function g(vec r)? What is it in 1d?

Answer 11

Question 12

What is the critical exponent (nu)?

Answer 12

Question 13

Is the occupation probability universal? Are the critical exponents? What does this mean?

Answer 13

Question 14

What is the idea of universality?

Answer 14