  We investigate zero and finite temperature properties of the one-dimensional
spin-glass model for vector spins in the limit of an infinite number m of spin
components where the interactions decay with a power, \sigma, of the distance.
A diluted version of this model is also studied, but found to deviate
significantly from the fully connected model. At zero temperature, defect
energies are determined from the difference in ground-state energies between
systems with periodic and antiperiodic boundary conditions to determine the
dependence of the defect-energy exponent \theta on \sigma. A good fit to this
dependence is \theta =3/4-\sigma. This implies that the upper critical value of
\sigma is 3/4, corresponding to the lower critical dimension in the
d-dimensional short-range version of the model. For finite temperatures the
large m saddle-point equations are solved self-consistently which gives access
to the correlation function, the order parameter and the spin-glass
susceptibility. Special attention is paid to the different forms of finite-size
scaling effects below and above the lower critical value, \sigma =5/8, which
corresponds to the upper critical dimension 8 of the hypercubic short-range
model.
