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Cluster - Statistical Mechanics

  1. Feb 22, 2007 #1
    1.The problem statement, all variables and given/known data
    A lattice in one dimension has N sites and is at temperature T. At each site there is an atom which can be in either of two energy states Ei = +/- E. When L consecutive atoms are in the +E state, we say they form a cluster of length L (provided that the atoms adjacent to the ends of the cluster are in the -E state). In the limit N=>infinity, compute the probability P(L) that a given site belongs to a cluster of length L.

    2. Relevant equations
    I'm trying to figure out how to write the equation that express the probaility P(L). This is my biggest problem. Maybe someone that has knowledge about Clusters in Statistical Mechanics can help me to understand this problem.

    3. The attempt at a solution
    My idea to solve the problem: Let L=4, for instance,

    ...(-E) (+E) (+E) (+E) (+E) (-E)...

    P(L) = P(4) = P(-) x 4P(+)^4 x P(-)
    But I don't know what is P(+ or -).
    Last edited: Feb 22, 2007
  2. jcsd
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