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Homework Help: Cluster Approximation for the Two-Dimensional Ising Model

  1. Nov 6, 2017 #1

    MathematicalPhysicist

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    1. The problem statement, all variables and given/known data
    In the attachments there is the question and its solution, it's problem 3.5.

    2. Relevant equations


    3. The attempt at a solution
    My question is how did they get the dimensionless Hamiltonian in both cases, and how did they explicitly calculated ##m## in both cases?

    I assume it's with ##m = \frac{\sum_{\sigma_i}\sigma_i e^{-\beta H}}{\sum e^{-\beta H}}##, but I really don't see how to get to the same terms as in the solution.

    Your help is appreciated!
    View attachment 214464 View attachment 214465
     
  2. jcsd
  3. Nov 9, 2017 #2

    MathematicalPhysicist

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    I can see that the pictures didn't get uploaded, so I am sending it again.
    Screenshot from 2017-11-06 16-26-56.png Screenshot from 2017-11-06 16-26-38.png
     
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