Is there a metamagnetic transition in a 2d electron gas subject to an in-plane magnetic field?

In this paper we consider the degree of spin-polarization in the ground state of a 2d electron system subject to an in-plane magnetic field. After briefly reviewing the Hartree-Fock results we present an analysis based on a summation of "ring" diagrams for the contribution to the correlation energy. We find that, in the "ring approximation" the system has: a high density regime in which the spin-polarization smoothly increases from zero to unity as the field is increased; a low density ferromagnetic regime in which the electrons are fully polarized even in the absence of a field; an intermediate regime in which the polarization initially increases smoothly as the field is increased from zero but eventually meets a first order metamagnetic transition at a density dependent magnetic field. The line of metamagnetic transitions terminates at the low density end at the first order ferromagnetic transition at r(s) approximate to 5.5 and at the high density end at a quantum critical end-point at r(s) approximate to 2.5. We speculate on the effects of correlations beyond the ring approximation.