Topics in Statistic Mechanics

Adv. Sta. Phy. Homework 1 Percolation Li,Zimeng PB06203182
p
p'
a
p
p
2a
The smallest generating structure is the blue
line
Fig 4.1
It's easily seen that p'= (4.1)
Taking
are occupied, we have
as an example, referring to the blue line in Fig 4.1, if all the up bonds
It the same when down bonds are all occupied. The third case is the case in Fig 4.1
where the marked (with p) bond is occupied, and the case of its counterpart. Therefore
we totally have 2
We now search for the fixed point in (4.1)
solutions for p
Because 0