  We calculate the geometric phase for an open system (spin-boson model) which
interacts with an environment (ohmic or nonohmic) at arbitrary temperature.
However there have been many assumptions about the time scale at which the
geometric phase can be measured, there has been no reported observation yet for
mixed states under nonunitary evolution. We study not only how they are
corrected by the presence of the different type of environments but also
estimate the corresponding times at which decoherence becomes effective. These
estimations should be taken into account when planning experimental setups to
study the geometric phase in the nonunitary regime, particularly important for
the application of fault-tolerant quantum computation.
