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2D Ising Model (analytical expressions)

  1. Jul 31, 2011 #1
    Hi all,

    I am doing a program to simulate the 2D Ising Model under the metropolis algorithm. In order to check my results I would like to compare them with the analytical expressions for the mean energy, magnetization, specific heat and magnetic susceptibility.

    I already found the expressions for the mean energy, magnetization and specific heat. However, when I plot the expression for the mean energy the result does not look right. I used the one in Huang's book. Concerning the magnetic susceptibility, I couldn't find any analytical expression...

    Anyone could give me some help? Thanks.

    Best regards!
     
  2. jcsd
  3. Aug 1, 2011 #2
    If you have the expression for the magnetisation for a given applied field you should be able to go from there to the susceptibility...
     
  4. Aug 2, 2011 #3
    Hi,

    Thank you for your reply. I am only interested in the case with B=0.

    The expression for the magnetization is [itex]M=[1-\sinh^{-4}(2/k_B T)]^{1/8}[/itex].

    The susceptibility is obtained from [itex]\chi = \frac{<M^2>- <M>^2}{k_B T}[/itex].

    But I don't know the analytical expression for [itex]\chi[/itex]...
     
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