  The zero-field isothermal susceptibility of the one-dimensional Ising model
with nearest-neighbor interactions and a finite number of spins is shown to
have a relatively simple singularity as the temperature approaches zero,
proportional only to the inverse temperature. This is in contrast to what is
seen throughout the literature for the inifinite chain: an essential
singularity that includes an exponential dependence on the inverse temperature.
Assuming an arbitrary (but finite) number of spins and retaining terms that are
usually considered ignorable in the thermodynamic limit, the analysis involves
nothing beyond straightforward series expansions, starting either from the
partition function for a closed chain in a magnetic field, obtained using the
transfer-matrix approach; or from the expression for the zero-field
susceptibility found via the fluctuation-dissipation theorem. In both cases,
the exponential singularity is exactly removed. In addition, the susceptibility
per spin is found to increase with the number of spins (except in the case of
noninteracting spins), a result which is also at variance with what is normally
reported for an infinite chain.
