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We consider a system of N∈ N mean-field interacting stochastic differential equations that are driven by Brownian noise and a single-site potential of the form z↦ z 4∕ 4− z 2∕ 2. The strength of the noise is measured by a small parameter ε> 0 (which we interpret as the temperature), and we suppose that the strength of the interaction is given by J> 0. Choosing the empirical mean (P: R N→ R, P x= 1∕ N∑ i x i) as the macroscopic order parameter for the system, we show that the resulting macroscopic Hamiltonian has two global minima, one at− m ε⋆< 0 and one at m ε⋆> 0. Following this observation, we are interested in the average transition time of the system to P− 1 (m ε⋆), when the initial configuration is drawn according to a probability measure (the so-called last-exit distribution), which is supported around the hyperplane P− 1 (− m ε⋆). Under the assumption of strong interaction, J> 1, the main result is a …