The Fortuin-Kasteleyn and heat-bath damage spreading temperatures T_{ FK}(p) and T_{ ds}(p) are studied on random bond Ising models of dimension two to five and as functions of the ferromagnetic interaction probability p; the conjecture that T_{ ds}(p) ~ T_{ FK}(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 T_{ FK}(p) transition line and the Nishimori line, [p_{ NL,FK},T_{ NL,FK}]. There are no finite size corrections for this intersection point. In dimension three, at the intersection concentration [p_{ NL,FK}] the damage spreading T_{ ds}(p) is found to be equal to T_{ FK}(p) to within 0.1%. For the other dimensions however T_{ ds}(p) is observed to be systematically a few percent lower than T_{ FK}(p).
Categories: cond-mat.stat-mech