Abstract
We study the inverse problem of inhomogeneous Ising lattices with a general spin which consists in finding the external potential required to produce a given profile of equilibrium single-site distributions. In particular, we extend a previously developed two-step procedure for simplifying the inverse problem to the case of many-spin interactions. The general procedure is applied to a special chain withh-spin interactions for which the inverse problem is, in principle and forh=2, 3, 4 also in practice, solvable exactly. Direct correlation functions of the proposed model have only short-range support.
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