First-order microcanonical transitions in finite mean-field models

Amicrocanonical first-order transition, connecting a clustered to a homogeneousphase, is studied from both the thermodynamic and the dynamical point of view for an N-bodyHamiltonian system with infinite-range couplings. In the microcanonical ensemble, specific heatcan be negative, but besides that, a microcanonical first-order transition displays a temperaturediscontinuity as the energy is varied continuously (a dual phenomenon to the latent heat in thecanonical ensemble). In the transition region, the entropy per particle exhibits, as a functionof the order parameter, two relative maxima separated by a minimum. The relaxation ofthe metastable state is shown to be ruled by an activation process induced by intrinsic finiteN fluctuations. In particular, numerical evidences are given that the escape time divergesexponentially with N, with a growth rate given by the entropy barrier.Introduction.