Two-dimensional electron gas near full polarization

We establish the consistency of the Fermi liquid description and find a relation between the Fermi liquid constants for a 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 a subleading ${(H}_c-{H)}^{1/2}$ dependence on the magnetic field. Also, the magnetization has a cusp with dependence of the type $(H-H_c{)+(H}_c-{H)}^{3/2}$ at $H<\mathrm{}{H}_c.$