Calculation of the average values of the Zeeman and dipole?dipole spin energies of a paramagnet at low temperatures

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For average values of the Hamiltonians of the Zeeman energy and the dipole-dipole spin interaction energy, a series is obtained representing the expansion of these averages in powers of the inverse temperature of the dipole-dipole interaction reservoir. The average values of specific operators appearing in the series as coefficients of the series are calculated from the complete density matrix of the system. These coefficients essentially are the low-temperature moments of resonance absorption lines of the spin system.