  In contrast to the infinite chain, the low-temperature expansion of a
one-dimensional free-field Ising model has a strong dependence on boundary
conditions. I derive explicit formula for the leading term of the expansion
both under open and periodic boundary conditions, and show they are related to
different distributions of partition function zeros on the complex temperature
plane. In particular, when the periodic boundary condition is imposed, the
leading coefficient of the expansion grows with size, due to the zeros
approaching the origin.
