Monte-Carlo calculations of phase transition temperature in the Ising model with long range interactions

The article deals with two-dimensional and three-dimensional Ising models with the long-range spin interactions. The intensity of interaction between the spins relies decreasing with distance $r$ as a power law $r^{-d-\sigma}$ with dimensional $d$ and parameter $\sigma$. The research are conducted by Monte-Carlo method with Metropolis algorithm using parallel computing techniques. On the basis of numerical simulation the dependence of the phase transition temperature on the parameter $\sigma$ is found. It is shown that at phase transition temperature decreases with increasing $\sigma$.