  Geometrical and topological properties of quantum ground state manifolds
permits to characterize phases of matter, and identify phase transitions. Here,
we study the effect of a quantum dissipative environment on the geometrical
properties of the ground state manifold of a single spin 1/2 in an external
effective magnetic field. We show that the quantum phase transition at zero
temperature in the model is associated with a universal metric singularity
related to the divergence of the spin susceptibility. The absence of transition
at finite temperature corresponds to a smooth variation of the associated
metric with temperature, without singular points.
