Phase Transition and Monopoles Densities in a Nearest Neighbors Two-Dimensional Spin Ice Model

In this work, we show that, due to the alternating orientation of the spins in the ground state of the artificial square spin ice, the influence of a set of spins at a certain distance of a reference spin decreases faster than the expected result for the long range dipolar interaction, justifying the use of the nearest neighbor two dimensional square spin ice model as an effective model. Using an extension of the model presented in ref. [Scientific Reports 5, 15875 (2015)], considering the influence of the eight nearest neighbors of each spin on the lattice, we analyze the thermodynamics of the model and study the monopoles and string densities dependence as a function of the temperature.