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

TL;DR

This paper presents an explicit solution to the inverse Ising problem for one-dimensional chains with arbitrary finite-range couplings, enabling the reconstruction of coupling constants from correlation data.

Contribution

It provides a novel explicit method for solving the inverse Ising problem in 1D chains with complex multispin and finite-range interactions.

Findings

Successfully reconstructs couplings for exponential and power-law interactions

Extends method to ladder systems and mean-field interactions

Demonstrates applicability to complex multispin 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.