Probability distribution function in the gas of paramagnetic particles

In this paper we consider a system of noninteracting paramagnetic particles with a spin S in a dc magnetic field. The exact expression for the probability distribution function of a transverse spin component is obtained for the gas in thermodynamic equilibrium. Dependences of the probability on the thermofield parameter βμH (β is the inverse temperature, μ is the Bohr magneton, H is a field strength) and S are investigated. It is shown that this distribution reflects the quantum nature of the spin and both the spin-wave and the classical approximation formulas are obtained