Random currents for signed interactions in the one-dimensional heterogeneous Ising model

The random current representation has been very successful in analyzing the ferromagnetic Ising model. In this article, we extend the method to the non-ferromagnetic case. To show its usefulness, we derive a covariance identity for the heterogeneous one-dimensional Ising model, which recovers the correct rate of exponential decay of covariances in the case of random i.i.d. interaction and external field.