  We present phase diagrams, free-energy landscapes, and order-parameter
distributions for a model spin-crossover material with a two-step transition
between the high-spin and low-spin states (a square-lattice Ising model with
antiferromagnetic-like nearest-neighbor and ferromagnetic-like long-range
interactions) [P. A. Rikvold et al., Phys. Rev. B 93, 064109 (2016)]. The
results are obtained by a recently introduced, macroscopically constrained
Wang-Landau Monte Carlo simulation method [C. H. Chan, G. Brown, and P. A.
Rikvold, Phys. Rev. E 95, 053302 (2017)]. The method's computational efficiency
enables calculation of thermodynamic quantities for a wide range of
temperatures, applied fields, and long-range interaction strengths. For
long-range interactions of intermediate strength, tricritical points in the
phase diagrams are replaced by pairs of critical end points and mean-field
critical points that give rise to horn-shaped regions of metastability. The
corresponding free-energy landscapes offer insights into the nature of
asymmetric, multiple hysteresis loops that have been experimentally observed in
spin-crossover materials characterized by competing short-range interactions
and long-range elastic interactions.
