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Homework Help: Statistical Thermodynamics - Help Wanted

  1. Feb 16, 2010 #1
    Statistical Thermodynamics - Help Wanted :(

    (My translation skills sucks, I hope it is understandable.)

    Three spins, placed at vertices of an equilateral triangle, are put in the external magnetic field with density B. Hamiltonian of the system:
    [tex] H = -J \sum_{<i,j>} s_{i} s_{j} - \gamma \hbar B \sum_{i=1}^3 s_{i} [/tex]

    where first sum runs over pairs of the nearest-neighbour spins and describes interactions between them, and the second sum represents spin interaction with external field; [tex] s_{i} [/tex] can take values between +1/2 and -1/2. Sketch possible states of the system and calculate the partition function! How much is the magnetic susceptibility of this triplet of spins system at T=300K ?
    Other data: [tex] J = 0.02 eV \gamma = e_{0}/m [/tex] , where [tex] e_{0} [/tex] and [tex] m [/tex] are electron charge and mass. Volume, taken by this triplet of spins is [tex] 0.1 nm^3 [/tex]

    My attempt of the solution was so unsuccessful that isn't worth wasting time writing it in latex. The problem is a form of Ising model; at class we did one problem of finding Z in 1D and much simpler hamiltonian. I thought I kind of understood it then, but it doesn't help me much with this problem.
    Help? Thnx in advance.
     
  2. jcsd
  3. Feb 17, 2010 #2

    Physics Monkey

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    Re: Statistical Thermodynamics - Help Wanted :(

    Hi asynja,

    I'm not sure what the point of this problem is exactly, but the system is simple enough with only 2^3 = 8 states that you can list all the energies for computing the partition function explicitly. Is this how you're approaching the problem?

    There is also a trick for rewriting the interaction term that makes the problem easier.
     
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