  A recently developed Quantum Monte Carlo algorithm based on the stochastic
evolution of Hartree-Fock states has been applied to compute the static
correlation functions of a one-dimensional model of attractively interacting
two component fermions. The numerical results have been extensively compared to
existing approximate approaches. The crossover to a condensate of pairs can be
identified as the first-order pair coherence extending throughout the whole
size of the system. The possibility of revealing the onset of the transition
with other observables such as the density-density correlations or the
second-order momentum space correlations is discussed.
