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Vitor Sessak and Rémi Monasson 2009 J. Phys. A: Math. Theor. 42 055001 doi:10.1088/1751-8113/42/5/055001
Vitor Sessak and Rémi Monasson
Show affiliationsWe present a systematic small-correlation expansion to solve the inverse Ising problem and 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.
05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
75.60.Ej Magnetization curves, hysteresis, Barkhausen and related effects
75.40.Mg Numerical simulation studies
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
82B80 Numerical methods (Monte Carlo, series resummation, etc.) (See also 65-XX, 81T80)
82D30 Random media, disordered materials (including liquid crystals and spin glasses)
Issue 5 (6 February 2009)
Received 26 September 2008, in final form 14 November 2008
Published 6 January 2009
Total article downloads: 387
Vitor Sessak and Rémi Monasson 2009 J. Phys. A: Math. Theor. 42 055001
