Metastability and anomalous behavior in the HMF Model: connections to nonextensive thermodynamics and glassy dynamics
نویسندگان
چکیده
We review some of the most recent results on the dynamics of the Hamiltonian Mean Field (HMF) model, a systems of N planar spins with ferromagnetic infiniterange interactions. We show, in particular, how some of the dynamical anomalies of the model can be interpreted and characterized in terms of the weak-ergodicity breaking proposed in frameworks of glassy systems. We also discuss the connections with the nonextensive thermodynamics proposed by Tsallis.
منابع مشابه
Glassy dynamics and nonextensive effects in the HMF model : the importance of initial conditions
In this work we discuss glassy dynamics and nonextensive thermodynamics in the context of the so called Hamiltonian Mean Field (HMF) model, a system of inertial spins with long-range interaction. This model and its generalizations has been intensively investigated in the last years for its anomalous dynamical behavior.1)–13) With respect to systems with short-range interactions, the dynamics an...
متن کاملMetastability in the Hamiltonian Mean Field model and Kuramoto model
We briefly discuss the state of the art on the anomalous dynamics of the Hamiltonian Mean Field model. We stress the important role of the initial conditions for understanding the microscopic nature of the intriguing metastable quasi stationary states observed in the model and the connections to Tsallis statistics and glassy dynamics. We also present new results on the existence of metastable s...
متن کاملGlassy dynamics in the HMF model
We discuss the glassy dynamics recently found in the meta-equilibrium quasi-stationary states (QSS) of the HMF model. The relevance of the initial conditions and the connection with Tsallis nonextensive thermostatistics is also addressed. c © 2004 Elsevier B.V. All rights reserved. PACS: 05.50.+q; 05.70.Fh; 64.60.Fr
متن کاملMetastable states, anomalous distributions and correlations in the HMF model
We study the microscopic dynamics of the metastable Quasi-Stationary States (QSS) in the Hamiltonian Mean Field (HMF) model, a Hamiltonian system of N classical inertial spins with infinite-range interactions which shows a second order phase transition. In order to understand the origin of metastability, which appears in an energy region below the critical point, we consider two different class...
متن کاملEffective spin-glass Hamiltonian for the anomalous dynamics of the HMF model
We discuss an effective spin-glass Hamiltonian which can be used to study the glassy-like dynamics observed in the metastable states of the Hamiltonian mean field (HMF) model. By means of the Replica formalism, we were able to find a self-consistent equation for the glassy order parameter which reproduces, in a restricted energy region below the phase transition, the microcanonical simulations ...
متن کامل