  We revisit the one-dimensional ferromagnetic Ising spin-chain with a finite
number of spins and periodic boundaries and derive analytically and verify
numerically its various stationary and dynamical properties at different
temperatures. In particular, we determine the probability distributions of
magnetization, the number of domain walls, and the corresponding residence
times for different chain lengths and magnetic fields. While we study finite
systems at thermal equilibrium, we identify several temperatures similar to the
critical temperatures for first-order phase transitions in the thermodynamic
limit. We illustrate the utility of our results by their application to
structural transitions in biopolymers having non-trivial intermediate
equilibrium states.
