Topics in Statistic Mechanics

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Adv. Sta. Phy. Homework 1 Percolation Li,Zimeng PB06203182 inside porous rocks in oil reservoirs. [3]Diffusion in Disordered Media Hydrogen atoms are known to diffuse through many solids, an effect which might become important for energy storage. A particularly simple disordered medium is our percolation lattice. [4]Gelation 3.Exact Solution on Cayley Tree Cayley Tree Bethe lattice, or Cayley tree, have every of its sites connected with z neighbours, but none of them form loops. See Fig 3.1 Fig 3.1 Cayley Tree As can be seen above, there is an origin site in the center, and around each site is its neighbours. Branches are all sites besides the origin site, and subbranches can also be defined similarly, but in the branch region. therefore no wonder Cayley Tree is infinite dimension. To get the percolation threshold of Cayley Tree, we start from the center, following the
Adv. Sta. Phy. Homework 1 Percolation Li,Zimeng PB06203182 path outward, to see if an infinitely large cluster is formed. We find z-1 new bonds emanating from every new site. So the probability that these new neighbours are occupied is p(z-1). If p(z-1)
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Topics in Statistic Mechanics

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