This paper adds a new perspective on the venerable Sherrington-Kirkpatrick (SK) spin glass model, which is a crucible of disorder and glassy behavior. It has applications not only in the physics of disordered materials, but also in AI (neural networks), brain function, combinatorial optimization, and machine learning, for example (see the book by Stein and Newman, Spin Glasses and Complexity, 2013). Here, it is shown that a dilute version of the model has a dilution-dependent scaling correction for its ground state energy (ie, optimal configuration), suggesting new inroads by which to study the model and its finite-size properties.

Different ways to reach the thermodynamic limit (N->infinity) in the SK-model. The diagonal corresponds to the original, undiluted model (all-to-all network), the horizontal corresponds to “sparse” Erdos-Reni networks of fixed degree c. The dilute SK (blue arrows) reaches the limit at constant density p=c/(N-1), with scaling corrections that vary with p.]