The Stochastic Models Method of Alexandrowicz and Its Implications

Assume an Ising model on a square lattice oiN = L X L spins. At site k on the lattice the possible spin orientations are = 1. Neighbor spins m and I interact with ferromagnetic energy 0) and the reciprocal temperature is defined by K = With the SM method one starts from an empty 

The set of parameters is determined prior to the simulation, thus defining 

One generates several samples with different sets of parameters, and the set leading to the lowest value of F d) is the optimal one in accordance with the minimum free energy principle (see Eq. [10]). That set is then used in the production runs. In principle, one can estimate the correct F by importance sampling (as in Eq. [71]) however satisfactory results for F have already been obtained from Eq. [80]. This method was improved later by Meirovitch, who calculated the transition probabilities differently, by looking ahead as with the scanning method. Finally we point out that the transformation from an Ising 

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