Finite T transverse magnetization of transverse Ising chain

[poiuyt]

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.

 

[king vitamin]

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.