  The statistical mechanics of a one-dimensional Ising model in thermal
equilibrium is well-established, textbook material. Yet, when driven far from
equilibrium by coupling two sectors to two baths at different temperatures, it
exhibits remarkable phenomena, including an unexpected 'freezing by heating.'
These phenomena are explored through systematic numerical simulations. Our
study reveals complicated relaxation processes as well as a crossover between
two very different steady-state regimes.
