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We introduce a general class of mean-field-like spin systems with randomcouplings that comprises both the Ising model on inhomogeneous dense randomgraphs and the randomly diluted Hopfield model. We are interested inquantitative estimates of metastability in large volumes at fixed temperatureswhen these systems evolve according to a Glauber dynamics, i.e.\ where spinsflip with Metropolis transition probabilities at inverse temperature $\beta$.We identify conditions ensuring that with high probability the system behaveslike the corresponding system where the random couplings are replaced by theiraverages. More precisely, we prove that the metastability of the former systemis implied with high probability by the metastability of the latter. Moreover,we consider relevant metastable hitting times of the two systems and find theasymptotic tail behaviour and the moments of their ratio. This work provides anextension of the results known for the Ising model on the Erd\H{o}s--R{\'e}nyirandom graph. The proofs use the potential-theoretic approach to metastabilityin combination with concentration inequalities.

Metastability of Glauber dynamics with inhomogeneous coupling disorder