Monte Carlo Simulation of 2D Ising Spin Glass with Power Law Decaying Interactions

We study the distance dependent interaction coupling in 2D in order to show how a spin glass phase transition occurs when couplings between far away spins are permitted by considering the Edwards–Anderson Ising spin glass model. The interaction coupling is a quenched random variable whose probability of being non-zero decays with distance between two spin sites $(p(J_{ij})\propto r_{ij}^{-\rho })$ . We study the model by changing ρ in three different regimes (ρ>2D, $\frac{4}{3} D < \rho < 2D$ , $\rho <\frac{4}{3} D$ ). We obtain a phase transition temperature for ρ=2,3,4.