We show that under the heat-bath Glauber dynamics for the ferromagnetic Ising model on a finite graph, the single spin expectation at a fixed time starting at the all-up configuration is not necessarily an increasing function of coupling constants.
"A remark on monotonicity for the Glauber dynamics on finite graphs." Proc. Japan Acad. Ser. A Math. Sci. 86 (2) 33 - 37, February 2010. https://doi.org/10.3792/pjaa.86.33