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Homework Help: 1D Ising ground state

  1. Jun 27, 2011 #1
    1. The problem statement, all variables and given/known data
    Find the ground state (stable configuration at T = 0) of the one-dimensional ising model with first and second neighbour intercations:

    [itex] H = -J_1 \sum_{i} s_i s_{i+1} -J_2 \sum_{i} s_i s_{i+2} [/itex]

    where [itex] s_i = \pm 1 [/itex]

    3. The attempt at a solution

    I really don't know what i should do.. i don't know what i must FIND, this is my problem!
    maybe i must find the Partition function and calculate the average magnetization ? so i say:

    [itex] Z = \sum_{s} \exp{[-\beta H]} = (2 \cosh(\beta J_1) \cosh(\beta J_2))^N [/itex]

    but seems that:

    [itex] <s>_{T=0} = \frac{ \sum_{s} \exp{[-\beta H]} \sum_{i}s_i } {\sum_{s} \exp{[-\beta H]}} =0 [/itex]

    i'm not intrested about solution, but i want to know what i must do---

    thanks all,
    Last edited: Jun 27, 2011
  2. jcsd
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