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\sect{State functions of spin 1/2 system}

Find the state functions ${E\left(T,B\right),M\left(T,B\right),
S\left(T,B\right)}$ for ${N}$ spins system:
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\[H=-\gamma B\sum_{a=1}^{N}\sigma_{t}^{a}\]
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Write the results for a weak magnetic field ${\gamma B<<T}$.
Especially find the magnetic susceptibility ${\chi}$ 
and ${ S \left(B \rightarrow 0\right)}$