  The collective properties of spin-crossover chains are studied.
Spin-crossover compounds contain ions with a low-spin ground state and low
lying high-spin excited states and are of interest for molecular memory
applications. Some of them naturally form one-dimensional chains. Elastic
interaction and Ising exchange interaction are taken into account. The
transfer-matrix approach is used to calculate the partition function, the
fraction of ions in the high-spin state, the magnetization, susceptibility,
etc., exactly. The high-spin-low-spin degree of freedom leads to collective
effects not present in simple spin chains. The ground-state phase diagram is
mapped out and compared to the case with Heisenberg exchange interaction. The
various phases give rise to characteristic behavior at nonzero temperatures,
including sharp crossovers between low- and high-temperature regimes. A
Curie-Weiss law for the susceptibility is derived and the paramagnetic Curie
temperature is calculated. Possible experiments to determine the exchange
coupling are discussed.
