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Two dimensional electron gas near full polarization

We establish the consistency of the Fermi liquid description and find a relation between Fermi liquid constants for the two dimensional electron system near the point of full polarization due to a parallel magnetic field $H$. Our results enable us to predict connections between different thermodynamic properties of the system. In particular, we find that near the point of full polarization $H_c$, the thermodynamic compressibility of the system experiences a jump with the subleading $(H_c-H)^{1/2}$ dependence on the magnetic field. Also, the magnetization has a cusp with the dependence of the type $(H-H_c) + (H_c-H)^{3/2}$ at $H<H_c$.