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Consider a system in which atoms are located in a regular lattice, each atom having a spin $1/2$ and an associated intrinsic magnetic moment $\mu_0>0$. Assume that each atom interacts only weakly with other atoms so that all the other atoms act as a heat reservior. If the system is placed in an external magnetic field $H_0 \hat{z}$, then the Hamiltonian is given by: $$\hat{H}=-\mu_0H_0\sum_i\sigma^z_i$$ where $\sigma_i^z$ are (the $z$ components of) the Pauli matrices, at the $i$th site.

For the magnetic moment $\mu= \pm\mu_0$, the corresponding magnetic energy of the atom is $E=\mp\mu_0 H_0$.

What would be the mean magnetic moment?

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