Size effect on the three state thermal hysteresis of a 2D spin crossover nanoparticles

In this report first we show, in a framework of the Ising-like model, a numerical simulation of a typical two step thermal transition obtained for a square lattice 12x12: a "first-step hysteresis" for a high spin fraction Nhs between 0 - 0,5 and at a higher temperature a "second-step hysteresis" with Nhs between 0.5 and 1. As long as we decrease the number of molecules the temperature range of the "second-step hysteresis" moves to a lower temperature, until is obtained, for a square of 4x4, a clear overlapped case with a three state behaviour. A detailed analys is on the role of the size system (4x4, 5x5, 6x6, 8x8 and 12x12) on the stability of this "Three state behaviour" is presented in this contribution. We study the influence of the surrounding environment for this specific thermal hysteresis. To solve the self-consistent equation related to the average value of the spin-operator , we use the density of the states calculated using a dynamic programming algorithm that will be presented in this paper.