Finite T transverse magnetization of transverse Ising chain

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SUMMARY

The discussion centers on calculating the finite temperature magnetization $$\langle\sigma_z\rangle$$ for the transverse field Ising model described by the Hamiltonian $$H=-J\sum_i\left(\sigma^x_i\sigma^x_{i+1}+g\sigma^z_i\right)$$. Participants debate whether the problem is classical or quantum, with the consensus leaning towards the quantum Ising chain. The recommended solution methods include the transfer matrix approach for classical cases and the more complex Jordan-Wigner and Bogoliubov transformations for quantum scenarios.

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  • Understanding of the transverse field Ising model
  • Familiarity with quantum mechanics principles
  • Knowledge of Jordan-Wigner and Bogoliubov transformations
  • Experience with statistical mechanics at finite temperatures
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  • Study the transfer matrix method for the classical Ising model
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Homework Statement


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.

Homework Equations

The Attempt at a Solution


I have to say, I'm a bit lost.
 
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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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