A Use The Partition Function To Find An Exact Expression

(a) Use the partition function to find an exact expression for the magnetization M and the susceptibility X = dM/dB as a function of temperature and magnetic field for the model system of magnetic nm tanh(mB/τ), as derived in (46) by another method. Here n is the particle concentration. The result is plotted in figure.

(b) Find the free energy and express the result as a function only of τ and the parameter x ≡ M/nm

(c) Show that the susceptibility is X = nm2/τ in the limit mB << τ,

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