Metastable states in a class of long-range Hamiltonian systems

Abstract

We numerically show that metastable states, similar to the Quasi Stationary States found in the so called Hamiltonian Mean Field Model, are also present in a generalized model in which $N$ classical spins (rotators) interact through ferromagnetic couplings decaying as $r^{-\alpha }$, where $r$ is their distance over a regular lattice. Scaling laws with $N$ are briefly discussed.

Latex 2e, 11 pages, 3 eps figures, contributed paper to the conf. "NEXT 2001", 23-30 May 2001, Cagliari (Italy), submitted to Physica A

References in corpus (4)

• Non-Gaussian equilibrium in a long-range Hamiltonian system
• Inequivalence of ensembles in a system with long range interactions
• Fingerprints of nonextensive thermodynamics in a long-range Hamiltonian system
• Chaos suppression in the large size limit for long-range systems

Cited by in corpus (29)

• Stability criteria of the Vlasov equation and quasi-stationary states of the HMF model
• Nonextensive statistical mechanics and economics
• Nonextensive Pesin identity. Exact renormalization group analytical results for the dynamics at the edge of chaos of the logistic map
• Nonergodicity and Central Limit Behavior for Long-range Hamiltonians
• Canonical Solution of Classical Magnetic Models with Long-Range Couplings
• Ensemble averages and nonextensivity at the edge of chaos of one-dimensional maps
• Hamiltonian dynamics reveals the existence of quasi-stationary states for long-range systems in contact with a reservoir
• Incomplete equilibrium in long-range interacting systems
• Metastable states, anomalous distributions and correlations in the HMF model
• Comment on "Critique of q-entropy for thermal statistics" by M. Nauenberg
• Metastability, negative specific heat and weak mixing in classical long-range many-rotator system
• Quasi-stationary states in low-dimensional Hamiltonian systems
• Mixing and equilibration: Protagonists in the scene of nonextensive statistical mechanics
• Glassy phase in the Hamiltonian Mean Field model
• Stationary states and fractional dynamics in systems with long range interactions
• Scaling with system size of the Lyapunov exponents for the Hamiltonian Mean Field model
• Controlling the Range of Interactions in the Classical Inertial Ferromagnetic Heisenberg Model: Analysis of Metastable States
• Stability of the entropy for superstatistics
• Generalization of the possible algebraic basis of $q$-triplets
• Thermodynamics is more powerful than the role to it reserved by Boltzmann-Gibbs statistical mechanics
• Emergence of a non trivial fluctuating phase in the XY model on regular networks
• Overdamped dynamics of long-range systems on a one-dimensional lattice: Dominance of the mean-field mode and phase transition
• Nonstandard entropy production in the standard map
• Effective spin-glass Hamiltonian for the anomalous dynamics of the HMF model
• On "Ergodicity and Central Limit Theorem in Systems with Long-Range Interactions" by Figueiredo et al
• Stationary state in N-body System with power law interaction
• Making thermodynamic functions of nanosystems intensive
• Non-Universal Finite Size Effects with Universal Infinite-Size Free Energy for the $\alpha$-XY model
• Numerical studies for an ab initio investigation into the Boltzmann prescription in statistical mechanics of large systems