Abstract
We study Ising chains with arbitrary multispin finite-range couplings, providing an explicitsolution of the associated inverse Ising problem, i.e. the problem of inferring the values ofthe coupling constants from the correlation functions. As an application, we reconstruct thecouplings of chain Ising Hamiltonians having exponential or power-law two-spin plusthree- or four-spin couplings. The generalization of the method to ladders and to Isingsystems where a mean-field interaction is added to general finite-range couplings is alsodiscussed.
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