State counting and low-temperature series

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Abstract
I present a simple numerical technique for evaluating the low-temperature expansion for discrete statistical systems. I begin with a recursive procedure on finite lattices to count the states of a given energy. Comparing these numbers on different lattice sizes, I extract coefficients for the infinite-volume series. I test the method with the three-dimensional Ising model, obtaining the expansion of the average energy through terms involving 34 excited bonds.