Heisenberg Integer Spin Chains in a Uniform Magnetic Field

We investigate both numerically and analytically the behavior of a spin-1 antiferromagnetic isotropic Heisenberg chain in an external uniform magnetic field. Extensive DMRG studies of chains up to N = 80 sites extend previous analyses and obtain the zero-temperature correlation functions. We argue that, despite the presence of a magnetic field, the model is still well described by an O(3) nonlinear σ-model. A saddle-point analysis, that also includes Gaussian fluctuations, is developed for the latter both at zero and finite temperatures. Its predictions are compared with those of the numerical analysis and with the existing experimental literature.