The study of diluted spin glasses may help solve some problems in computer science and physics. In this talk, I shall introduce the diluted Shcherbina–Tirozzi (ST) model with a quadratic Hamiltonian, for which we computed the free energy at all temperatures and external field strengths. In particular, we showed that the free energy can be expressed in terms of the weak limits of the quenched spin variances and identified these weak limits as the unique fixed points of a recursive distributional operator. The talk is based on a joint work with Wei-Kuo Chen and Arnab Sen.

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Last updated: 19 Jul 2024