A correlation bound for the one-dimensional heterogeneous Ising model

We derive a new upper bound for the correlations in a heterogeneous one-dimensional Ising model with free boundary conditions. The new upper bound quantifies the simultaneous decay of correlations due to weakness of nearest-neighbor coupling constants and the effect of external fields. The proof constitutes an application of random currents to a non-ferromagnetic Ising model.

💡 Research Summary

The paper studies the one‑dimensional heterogeneous Ising model on a finite interval ({0,\dots ,N}) with free boundary conditions. Each nearest‑neighbour edge ((x,x+1)) carries a non‑negative coupling constant (J_x) and each site (x) carries an external field (h_x\in\mathbb R). The Hamiltonian is
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