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<H_c.