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Finite T transverse magnetization of transverse Ising chain

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  1. Mar 8, 2015 #1
    1. The problem statement, all variables and given/known data
    Consider the transverse field Ising model, with

    $$H=-J\sum_i\left(\sigma^x_i\sigma^x_{i+1}+g\sigma^z_i\right)$$

    I have to calculate the magnetization $$\langle\sigma_z\rangle$$ at finite temperature.

    2. Relevant equations


    3. The attempt at a solution
    I have to say, I'm a bit lost.
     
  2. jcsd
  3. Mar 10, 2015 #2

    king vitamin

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    Gold Member

    Classical or quantum? If classical, have you seen the transfer matrix solution of the regular Ising model?

    If this is the quantum Ising chain, the only method I know to solve this is quite involved, and involves Jordan-Wigner and Bogoliubov transforms. If this is homework I would guess you would've been given more info for how to solve it.
     
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