Small-correlation expansions for the inverse Ising problem

Vitor Sessak (1) , Rémi Monasson (1)

1 LPTENS - Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure]

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.

Domaines: Systèmes désordonnés et réseaux de neurones [cond-mat.dis-nn]; Mécanique statistique [cond-mat.stat-mech]

Vitor Sessak, Rémi Monasson. Small-correlation expansions for the inverse Ising problem. Journal of Physics A: Mathematical and Theoretical, 2009, 42, pp.055001. ⟨10.1088/1751-8113/42/5/055001⟩. ⟨hal-00340939⟩