Topics in Statistic Mechanics
Topics in Statistic Mechanics
Topics in Statistic Mechanics
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Adv. Sta. Phy. Homework 1 Percolation Li,Zimeng PB06203182<br />
<strong>in</strong>side porous rocks <strong>in</strong> oil reservoirs.<br />
[3]Diffusion <strong>in</strong> Disordered Media<br />
Hydrogen atoms are known to diffuse through many solids, an effect which might<br />
become important for energy storage. A particularly simple disordered medium is our<br />
percolation lattice.<br />
[4]Gelation<br />
3.Exact Solution on Cayley Tree<br />
Cayley Tree<br />
Bethe lattice, or Cayley tree, have every of its sites connected with z neighbours, but<br />
none of them form loops. See Fig 3.1<br />
Fig 3.1<br />
Cayley Tree<br />
As can be seen above, there is an orig<strong>in</strong> site <strong>in</strong> the center, and around each site is its<br />
neighbours. Branches are all sites besides the orig<strong>in</strong> site, and subbranches can also be<br />
def<strong>in</strong>ed similarly, but <strong>in</strong> the branch region.<br />
therefore no wonder Cayley Tree is <strong>in</strong>f<strong>in</strong>ite dimension.<br />
To get the percolation threshold of Cayley Tree, we start from the center, follow<strong>in</strong>g the
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