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Ferromagnetism of electron gas

In current work, we investigate the density and temperature dependence of polarization parameter; using the relativistic formalism for the electron-electron interaction within the Fermi liquid model. we calculate the spin dependent scattering matrix elements in relativistic region, and then obtain the non-relativistic behavior to study the magnetic properties of an electron gas. By varying the polarization parameter, we minimized the free energy and then obtain the polarization of the system as a function of density and temperature. At zero temperature the exact results for polarization and magnetic susceptibility have obtained. It has been shown that for a given temperature (density) there is critical density (temperature) that the ferromagnetic phase can appears in electron gas. Our results show that at nonzero temperatures and in very low and very high densities the ferromagnetism phase can not be exist.