Nonequilibrium phase transitions in systems with long-range interactions.
We introduce a generalized Hamiltonian mean field model-an XY model with both linear and quadratic coupling between spins and explicit Hamiltonian dynamics. In addition to the usual paramagnetic and ferromagnetic phases, this model also possesses a nematic phase. The generalized Hamiltonian mean field model can be solved explicitly using Boltzmann-Gibbs statistical mechanics, in both canonical and microcanonical ensembles. However, when the resulting microcanonical phase diagram is compared with the one obtained using molecular dynamics simulations, it is found that the two are very different. We will present a dynamical theory which allows us to explicitly calculate the phase diagram obtained using molecular dynamics simulations without any adjustable parameters. The model illustrates the fundamental role played by dynamics as well the inadequacy of Boltzmann-Gibbs statistics for systems with long-range forces in the thermodynamic limit.
Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, CEP 91501-970, Porto Alegre, Rio Grande do Sul, Brazil.
Tarcísio N
TN
Teles
Fernanda P da C
FP
Benetti
Renato
R
Pakter
Yan
Y
Levin