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Herein, the collective effects of spin polarization in a degenerate electron gas of an arbitrary space dimension are discussed. We consider these low-dimensional systems in light of potential wells (rectangular or cylindrical), and as a two- or one-dimensional oscillator system with the second (and third) spatial dimension proportional to the oscillator’s length. The concept of “intermediate” sizes ν = 6, 5, 4 corresponding to the quasi-low dimensions ν* = 0, 1, 2, contrary to “pure” space dimensions ν = 1, 2 is introduced. A general effect of the space dimension upon the spontaneous polarization in electron Fermi gas is detected.

An Effect of the Space Dimension of Electron Fermi Gas upon the Spin Ordering in Clusters and Nanoparticles