Inverse Ising problem for one-dimensional chains with arbitrary finite-range couplings

Abstract

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.

Published version, typos corrected

References in corpus (3)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• The Ising Model for Neural Data: Model Quality and Approximate Methods for Extracting Functional Connectivity
• Small-correlation expansions for the inverse Ising problem

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• Ising chains with competing interactions in presence of long-range couplings
• Beyond inverse Ising model: structure of the analytical solution for a class of inverse problems
• Computation of microcanonical entropy at fixed magnetization without direct counting
• On the typical properties of inverse problems in statistical mechanics
• Metastable and scaling regimes of a one-dimensional Kawasaki dynamics
• Phase diagram of the one-dimensional three-state Potts model with an additional mean-field interaction