  We calculate the geometric phase of a spin-1/2 particle coupled to an
external environment comprising N spin-1/2 particle in the framework of open
quantum systems. We analyze the decoherence factor and the deviation of the
geometric phase under a nonunitary evolution from the one gained under an
unitary one. We show the dependence upon the system's and bath's parameter and
analyze the range of validity of the perturbative approximation. Finally, we
discuss the implications of our results.
