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The Fortuin-Kasteleyn and heat-bath damage-spreading temperatures TFK(p) and TDS(p) are studied on random-bond Ising models of dimensions 2–5 and as functions of the ferromagnetic interaction probability p; the conjecture that TDS(p)∼TFK(p) is tested. It follows from a statement by Nishimori that in any such system, exact coordinates can be given for the intersection point between the Fortuin-Kasteleyn TFK(p) transition line and the Nishimori line [pNL,FK,TNL,FK]. There are no finite-size corrections for this intersection point. In dimension 3, at the intersection concentration [pNL,FK], the damage spreading TDS(p) is found to be equal to TFK(p) to within 0.1%. For the other dimensions, however, TDS(p) is observed to be systematically a few percent lower than TFK(p).
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