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maybe someone can help me with this problem?

## Homework Statement

A system consist of

*N*Atoms that have a magnetic moment

*m*. The Hamiltonian in the presence of a magnetic field

*H*is

$$\mathcal{H}(p,q) - mH \sum_{i=1}^N cos(\alpha_{i})$$

where ##\alpha_i## is the angle between the magnetic field and the atom

*i.*

Show that the induced magnetisationt

*M*is:

$$M=Nm\coth(\theta-\frac 1 \theta), \theta=\frac {mH}{ k_BT}$$

## Homework Equations

Magnetisation ##M=-\frac {\partial F} {\partial H}##

Free energy ##F=-k_B\ln(Z)##

## The Attempt at a Solution

##Z=Z_{mech}* Z_{magn}##

I don't know how to calculate the magnetic partition function.