Monotonicity of relaxation time for ferromagnetic Ising Glauber dynamics

Let $G$ be any graph equipped with a ferromagnetic Ising model, with couplings $J_{xy}$, and let $\tau_2$ denote the relaxation time of its Glauber dynamics. Peres's monotonicity conjecture. For the ferromagnetic Ising model on any graph, the relaxation time $\tau_2$ is an increasing function of any of the couplings $J_{xy}$. This conjecture asks how the relaxation time depends on interaction strengths; the paper proves the corresponding monotonicity result when $G$ is a cycle, while the assertion for arbitrary graphs is left open in the source.