Inverse Ising problem for one-dimensional chains with arbitrary   finite-range couplings
  We study Ising chains with arbitrary multispin finite-range couplings, providing an explicit solution of the associated inverse Ising problem, i.e. the problem of inferring the values of the coupling constants from the correlation functions. As an application, we reconstruct the couplings of chain Ising Hamiltonians having exponential or power-law two-spin plus three- or four-spin couplings. The generalization of the method to ladders and to Ising systems where a mean-field interaction is added to general finite-range couplings is as well as discussed. 
Giacomo Gori, Andrea Trombettoni
cond-mat.stat-mech physics.data-an