Thermal phase transitions in Artificial Spin-Ice

We use the sixteen vertex model to describe bi-dimensional artificial spin ice (ASI). We find excellent agreement between vertex densities in fifteen differently grown samples and the predictions of the model. Our results demonstrate that the samples are in usual thermal equilibrium away from a critical point separating a disordered and an anti-ferromagnetic phase in the model. The second-order phase transition that we predict suggests that the spatial arrangement of vertices in near-critical ASI should be studied in more detail in order to verify whether they show the expected space and time long-range correlations.