  we investigate the thermodynamic properties of weakly anisotropic disordered
magnetic chains where the nearest-neighbor Heisenberg exchange coupling is the
dominant spin-spin interaction. In addition to the exchange interaction, there
is single-ion anisotropy with the direction of the easy axis being the same for
all spins. The analysis is carried out in the limit S >> 1, where S denotes the
ionic spin, and in the temperature range T << JaveS, where Jave is the average
magnitude of the exchange interaction. It is assumed that the independent boson
picture is appropriate so that the thermodynamic properties of the chain are
those of a gas of weakly interacting magnons whose frequencies are obtained
from linearized equations of motion for the spins. The =+/-J model is studied
in detail with both random and non-random anisotropy. Particular emphasis is
placed on the existence
