We study the Ising model on $\mathbb{Z}^{2}$ and show, via numerical simulation, that allowing interactions between spins separated by distances $1$ and $m$ (two ranges), the critical temperature, $ T_c (m) $, converges monotonically to the critical temperature of the Ising model on $\mathbb{Z}^4$ as $ m \to \infty $. Only interactions between spins located in directions parallel to each coordinate axis are considered... (read more)
PDF