Metastable States of the Classical Inertial Infinite-Range-Interaction Heisenberg Ferromagnet: Role of Initial Conditions

Abstract

A system of $N$ classical Heisenberg-like rotators, characterized by infinite-range ferromagnetic interactions, is studied numerically within the microcanonical ensemble through a molecular-dynamics approach. Such a model, known as the classical inertial infinite-range-interaction Heisenberg ferromagnet, exhibits a second-order phase transition within the standard canonical-ensemble solution. The present numerical analysis, which is restricted to an energy density slightly below criticality, compares the effects of different initial conditions for the orientations of the classical rotators. By monitoring the time evolution of the kinetic temperature, we observe that the system may evolve into a metastable state (whose duration increases linearly with $N$), in both cases of maximal and zero initial magnetization, before attaining a second plateau at longer times. Since the kinetic temperatures associated with the second plateau, in the above-mentioned cases, do not coincide, the system may present a three-plateaux (or even more complicated) structure for finite $N$. To our knowledge, this has never before been observed on similar Hamiltonian models, such as the XY version of the present model. It is also shown that the system is sensitive to the way that one breaks the symmetry of the paramagnetic state: different nonzero values for the initial magnetization may lead to sensibly distinct evolutions for the kinetic temperature, whereas different situations with zero initial magnetization all lead to the same structure.Comment: Communicated at the International Workshop on {\it Trends and Perspectives in Extensive and Non-Extensive Statistical Mechanics}, held in November 19-21, 2003, in Angra dos Reis, Brazil. Submitted to a Physica A issue dedicated to the event, and edited by E.M.F. Curado, H.J. Herrmann and M. Barbosa. 10 pages including 4 figure