This contribution, motivated by an experimental study of the influence of long-range interactions on the hysteresis loop, presents a theoretical study of spin-state transitions within the framework of an Ising-like model. The Hamiltonian includes both short- and long-range interactions and takes into account different degeneracies between molecular states. The problem is solved exactly for one-dimensional systems by using a transfer matrix method and the effects of temperature, long- and short-range interactions, and system size (number of molecules) are analysed in depth. The width of the thermal hysteresis loop of spin-crossover compounds decreases when reducing the long-range interactions, down to a critical value, calculated for the first time in this contribution, at which the hysteresis vanishes. This dependence is similar to the one generated by the decrease in short-range interactions assuming that the corresponding variation is proportional. An increase in the system size contributes to a larger influence of long-range interactions and the hysteretic loop approaches a rectangular shape and reaches a saturation width, which is predicted for the first time. These results are important for the design of novel spin-crossover materials featuring sharp spin transitions along with wide hysteresis loops, which are particularly suited for potential applications in display and data storage devices.