  Quantum Monte Carlo (QMC) techniques are used to provide an
approximation-free investigation of the phases of the one-dimensional
attractive Hubbard Hamiltonian in the presence of population imbalance. The
temperature at which the "Fulde-Ferrell-Larkin-Ovchinnikov" (FFLO) phase is
destroyed by thermal fluctuations is determined as a function of the
polarization. It is shown that the presence of a confining potential does not
dramatically alter the FFLO regime, and that recent experiments on trapped
atomic gases likely lie just within the stable temperature range.
