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

TL;DR

This paper demonstrates that in a two-dimensional artificial square spin ice, the influence of spins diminishes rapidly with distance, validating the use of a nearest neighbor model to study monopole and string densities across temperatures.

Contribution

The study extends the nearest neighbor model to include eight neighbors, analyzing thermodynamics and monopole/string densities, showing faster decay of spin influence than expected for dipolar interactions.

Findings

Rapid decay of spin influence supports nearest neighbor approximation

Monopole and string densities vary with temperature

Nearest neighbor model effectively captures thermodynamic behavior

Abstract

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.