An interacting electron liquid in two (2D) and three (3D) dimensions may undergo a paramagnetic-to-ferromagnetic quantum spin polarization transition at zero applied magnetic field, driven entirely by exchange interactions, as the system density ($n$) is decreased. This is known as Bloch ferromagnetism. We show theoretically that the application of an external magnetic field ($B$), which directly spin polarizes the system through Zeeman spin splitting, has an interesting effect on Bloch ferromagnetism if the applied field and carrier density are both decreased (from some initial applied high magnetic field at a high carrier density) in a power-law manner, $B\sim n^p$. For $p<p_c$, with $p_c=1(2/3)$ in $2\left(3\right)\mathrm{D}$, the system remains either fully spin polarized or undergoes a single transition from a partially spin-polarized (with two Fermi surfaces corresponding to spin up and down electrons) to a fully spin-polarized state (with a single Fermi surface of one spin) as the density and field decrease, depending on whether the starting point is partially spin polarized or fully spin polarized. However, for $p>p_c$, the system may undergo two transitions if starting from the fully spin-polarized state: first, a weak second-order transition at high density and field from the field-induced fully polarized phase to the partially polarized phase; and then, at a lower field and density, a reentrant first-order transition back to the fully spin-polarized phase again with a single Fermi surface.

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• Composite fermions
• Fermi surface
• Ferromagnetism
• Zeeman effect