  Calculating the density-density correlation function for disordered wires, we
study localization properties of wave functions in a magnetic field. The
supersymmetry technique combined with the transfer matrix method is used. It is
demonstrated that at arbitrarily weak magnetic field the far tail of the wave
functions decays with the length $L_{{\rm cu}}=2L_{{\rm co}}$, where $L_{{\rm
co}}$ and $L_{{\rm cu}}$ are the localization lengths in the absence of a
magnetic field and in a strong magnetic field, respectively. At shorter
distances, the decay of the wave functions is characterized by the length
$L_{{\rm co}}$. Increasing the magnetic field broadens the region of the decay
with the length $L_{{\rm cu}}$, leading finally to the decay with $L_{{\rm
cu}}$ at all distances. In other words, the crossover between the orthogonal
and unitary ensembles in disordered wires is characterized by two localization
lengths. This peculiar behavior must result in two different temperature
regimes in the hopping conductivity with the boundary between them depending on
the magnetic field.
