First-order microcanonical transitions in finite mean-field models

¹ UMR-CNRS 6171 - Université d'Aix-Marseille III Av. Esc. Normandie-Niemen, 13397 Marseille Cedex 20, France
² Dipartimento d'Energetica “S. Stecco” and CSDC, Università di Firenze, and INFN and INFM - via S. Marta 3, 50139 Firenze, Italy
³ Istituto Nazionale d'Ottica Applicata - Largo E. Fermi 6, 50125 Firenze, Italy

Received: 12 January 2004
Accepted: 8 April 2004

Abstract

A microcanonical first-order transition, connecting a clustered to a homogeneous phase, is studied from both the thermodynamic and the dynamical point of view for an N-body Hamiltonian system with infinite-range couplings. In the microcanonical ensemble, specific heat can be negative, but besides that, a microcanonical first-order transition displays a temperature discontinuity as the energy is varied continuously (a dual phenomenon to the latent heat in the canonical ensemble). In the transition region, the entropy per particle exhibits, as a function of the order parameter, two relative maxima separated by a minimum. The relaxation of the metastable state is shown to be ruled by an activation process induced by intrinsic finite N fluctuations. In particular, numerical evidences are given that the escape time diverges exponentially with N, with a growth rate given by the entropy barrier.