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The problem of stability of saturated and nonsaturated ferromagnetism in the Hubbard model is considered in terms of the one-particle Green's functions. Approximations by Edwards and Hertz and some versions of the self-consistent approximations based on the 1 / z expansion are considered. The account of longitudinal fluctuations turns out to be essential for description of the nonsaturated state. The corresponding pictures of density of states are obtained. "Kondo" density-of-states singularities owing to spin-flip processes are analyzed. The critical electron concentrations for instabilities of saturated ferromagnetism and paramagnetic state are calculated for various lattices. Drawbacks of various approximations are discussed. A comparison with the results of previous works is performed.

In this paper, we investigated the magnetocaloric effect (MCE) in one-dimensional magnets with different types of ordering in the Ising model, Heisenberg, XY -model, the standard, planar, and modified Potts models. Exact analytical solutions to MCE as functions of exchange parameters, temperature, values and directions of an external magnetic field are obtained. The temperature and magnetic field dependences of MCE in the presence of frustrations in the system in a magnetic field are numerically computed in detail.