  The recently measured spin susceptibility of the two dimensional electron gas
exhibits a strong dependence on temperature, which is incompatible with the
standard Fermi liquid phenomenology. Here we show that the observed temperature
behavior is inherent to ballistic two dimensional electrons. Besides the
single-particle and collective excitations, the thermodynamics of Fermi liquid
systems includes effects of the branch-cut singularities originating from the
edges of the continuum of pairs of quasiparticles. As a result of the
rescattering induced by interactions, the branch-cut singularities generate
non-analyticities in the thermodynamic potential which reveal themselves in
anomalous temperature dependences. Calculation of the spin susceptibility in
such a situation requires a non-perturbative treatment of the interactions. As
in high-energy physics, a mixture of the collective excitations and pairs of
quasiparticles can be effectively described by a pole in the complex momentum
plane. This analysis provides a natural explanation for the observed
temperature dependence of the spin susceptibility, both in sign and magnitude.
