Partition function in magnetism

When the individual particles of the system have magnetic moments /xh then their energies in the presence of a field B are 

If A is the number of magnetic moments per unit volume, the magnetisation becomes expressed as 

However, the magnetic moment is a vector and the magnetic susceptibility a second-rank tensor so that the rigorous transcription is 

Important expressions of statistical thermodynamics in magnetism are collected in Table 2.10. 

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