Effective Thermodynamics of Artificial Spin Ice*

We analyze the effective thermodynamics of artificial spin ice: a recently realized lattice of nanoscale single-domain ferromagnetic islands that are arrayed along the edges of a square lattice[1]. After demagnetization, the moments in this model system have a static disordered configuration similar to the frozen state of the spin ice materials. We demonstrate that this athermal state has extensive degeneracy and we introduce a formalism that can predict both the entropy and an effective temperature. The theory also predicts the populations of local states and short-distance correlations of this ice-like system with no adjustable parameters. \newline \newline References: \newline [1] R.~F. Wang, C.~Nisoli, R.~S. Freitas, J.~Li, W.~McConville, B.~J. Cooley, M.~S. Lund, N.~Samarth, C.~Leighton, V.~H. Crespi and P.~Schiffer, Nature (London) {\bf 439}, 303.