One-dimensional Ising-like systems: an analytical investigation of the static and dynamic properties, applied to spin-crossover relaxation

We investigate the dynamical properties of the 1-D Ising-like Hamiltonian t aking into account short and long range interactions, in order to predict t he static and dynamic behavior of spin crossover systems. The stochastic tr eatment is carried out within the frame of the local equilibrium method [1] . The calculations yield, at thermodynamic equilibrium, the exact analytic expression previously obtained by the transfer matrix technique [2]. We mai nly discuss the shape of the relaxation curves: (i) for large (positive) va lues of the short range interaction parameter, a saturation of the relaxati on curves is observed, reminiscent of the behavior of the width of the stat ic hysteresis loop [3]; (ii) a sigmoidal (self-accelerated) behavior is obt ained for large enough interactions of any type (iii) the relaxation curves exhibit a sizeable tail (with respect to the mean-field curves) which is c learly associated with the transient onset of first-neighbor correlations i n the system, due to the effect of short-range interactions. The case of ne gative short-range interaction is briefly discussed in terms of two-step pr operties.