A comparative study between Monte Carlo entropic sampling method and local mean field investigations of thermal properties of spin-crossover nanoparticles based on Ising-like model

The thermally induced transitions between low-spin (LS) and high-spin (HS) configurations of spin-crossover (SCO) nanoparticles are simulated, focusing on the effects of localized surface and bulk interactions on the average magnetization of 2D square lattices. The thermal behaviors and hysteresis cycles are investigated within the framework of the Ising model Hamiltonian and are conducted following two approaches: local mean field approximation (LMFA) and Monte Carlo entropic sampling (MCES) techniques. The results obtained by these two methods are compared for the two square lattice sizes, 6 $$ \times $$ 6 and 7 $$ \times $$ 7. Thus, when the bulk-surface interaction term is set to zero, the two approaches lead to identical values of the surface and bulk transition temperatures separated by a long intermediate plateau in both cases. Although hysteresis curves exhibit a similar shape, LMFA shows slightly larger widths $$ \Delta T $$ than MCES. On increasing bulk-surface interaction term, the two methods lead to different shifts in equilibrium temperature values for both bulk and surface components, respectively, to lower and higher values by MCES. In general, it is found that LMFA shifts surface equilibrium temperature differently to lower values and enhances the hysteresis effect, particularly for surface molecules. On the other hand, for the 7 $$ \times $$ 7 square lattice, the equilibrium temperatures are slightly higher by 1.5% and 3.2% for bulk and surface molecules, respectively, with a narrower hysteresis width in the surface. Moreover, with the MCES method, an abrupt transition instead of a hysteresis transition is calculated for surface molecules ($$ \Delta T_{surf}^{MCES}=0 $$ K).