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Frustrated arrays of interacting single-domain nanomagnets provide importantmodel systems for statistical mechanics, because they map closely ontowell-studied vertex models and are amenable to direct imaging and customengineering. Although these systems are manifestly athermal, we demonstratethat the statistical properties of both hexagonal and square lattices can bedescribed by an effective temperature based on the magnetostatic energy of thearrays. This temperature has predictive power for the moment configurations andis intimately related to how the moments are driven by an oscillating externalfield.

Effective Temperature in an Interacting, Externally Driven, Vertex System: Theory and Experiment on Artificial Spin Ice