Small-correlation expansions for the inverse Ising problem

Abstract

We present a systematic small-correlation expansion to solve the inverse Ising problem: find a set of couplings and fields corresponding to a given set of correlations and magnetizations. Couplings are calculated up to the third order in the correlations for generic magnetizations, and to the seventh order in the case of zero magnetizations; in addition we show how to sum some useful classes of diagrams exactly. The resulting expansion outperforms existing algorithms on the Sherrington-Kirkpatrick spin-glass model.

To appear in J. Phys. A

References in corpus (2)

• Weak pairwise correlations imply strongly correlated network states in a neural population
• Strongly Correlated Electron Materials: Dynamical Mean-Field Theory and Electronic Structure

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