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We study the elastic properties of thermal networks of Hookean springs. In the purely mechanical limit, such systems are known to have vanishing rigidity when their connectivity falls below a critical, isostatic value. In this work we show that thermal networks exhibit a non-zero shear modulus G well below the isostatic point, and that this modulus exhibits an anomalous, sublinear dependence on temperature T. At the isostatic point, G increases as the square-root of T, while we find G ∝ T^αdoi:10.1103/physrevlett.111.095503 pmid:24033046 fatcat:dkb6n4kjxreohp4cwwggsaeaiq