d'Dimensional classical Heisenberg model with arbitrarily ranged interactions: Lyapunov exponents and distributions of momenta and energies

Rodriguez Mesas, Antonio and Dantas Nobre, Fernando and Tsallis, Constantino (2019). d'Dimensional classical Heisenberg model with arbitrarily ranged interactions: Lyapunov exponents and distributions of momenta and energies. "Entropy" ; pp. 347-348. ISSN 1099-4300. https://doi.org/10.3390/e21010031.

Description

Title: d'Dimensional classical Heisenberg model with arbitrarily ranged interactions: Lyapunov exponents and distributions of momenta and energies
Author/s:
  • Rodriguez Mesas, Antonio
  • Dantas Nobre, Fernando
  • Tsallis, Constantino
Item Type: Article
Título de Revista/Publicación: Entropy
Date: January 2019
ISSN: 1099-4300
Subjects:
Freetext Keywords: complex Hamiltonian systems; nonextensive statistical mechanics; long-ranged-interacting thermostatistics; lyapunov exponents
Faculty: E.T.S. de Ingeniería Aeronáutica y del Espacio (UPM)
Department: Matemática Aplicada a la Ingeniería Aeroespacial
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

We numerically study the first-principle dynamics and thermostatistics of a d-dimensional classical inertial Heisenberg ferromagnetic model ( d=1,2,3 ) with interactions decaying with the distance rij as 1/rαij ( α≥0 ), where the limit α=0 ( α→∞ ) corresponds to infinite-range (nearest-neighbour) interactions, and the ratio α/d>1 ( 0≤α/d≤1 ) characterizes the short-ranged (long-ranged) regime. By means of first-principle molecular dynamics we study: (i) The scaling with the system size N of the maximum Lyapunov exponent λ in the form λ∼N−κ , where κ(α/d) depends only on the ratio α/d ; (ii) The time-averaged single-particle angular momenta probability distributions for a typical case in the long-range regime 0≤α/d≤1 (which turns out to be well fitted by q-Gaussians), and (iii) The time-averaged single-particle energies probability distributions for a typical case in the long-range regime 0≤α/d≤1 (which turns out to be well fitted by q-exponentials). Through the Lyapunov exponents we observe an intriguing, and possibly size-dependent, persistence of the non-Boltzmannian behavior even in the α/d>1 regime. The universality that we observe for the probability distributions with regard to the ratio α/d makes this model similar to the α -XY and α -Fermi-Pasta-Ulam Hamiltonian models as well as to asymptotically scale-invariant growing networks.

More information

Item ID: 67740
DC Identifier: https://oa.upm.es/67740/
OAI Identifier: oai:oa.upm.es:67740
DOI: 10.3390/e21010031
Official URL: https://www.mdpi.com/1099-4300/21/1/31
Deposited by: Memoria Investigacion
Deposited on: 02 Dec 2021 08:52
Last Modified: 02 Dec 2021 08:52
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