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Article overview
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Emergence of a collective crystal in a classical system with long-range interactions | Alessio Turchi
; Duccio Fanelli
; Xavier Leoncini
; | Date: |
7 May 2015 | Abstract: | A one-dimensional long-range model of classical rotators with an extended
degree of complexity, as compared to paradigmatic long-range systems, is
introduced and studied. Working at constant density, in the thermodynamic limit
one can prove the equivalence with the Hamiltonian Mean Field model (HMF) and
$alpha$-HMF: a second order phase transition is indeed observed at the
critical energy threshold $varepsilon_c=0.75$. Conversely, when the
thermodynamic limit is performed at infinite density (while keeping the length
of the hosting interval $L$ constant), the critical energy $varepsilon_c$ is
modulated as a function of $L$. At low energy, a self-organized collective
crystal phase is reported to emerge. According to numerics, the crystal phase
is split into two distinct regimes depending on the value of the energy per
particle $varepsilon$: for small $varepsilon$, particles are exactly located
on the lattice sites. At variance, above a given energy threshold
$varepsilon{*}$, such correspondence is broken and particles can travel from
one site to the other. However, $varepsilon{*}$ does not signal a genuine
transition but rather reflects the finite time of observation, as imposed in
the simulations. Transport between adjacent crystal sites occurs at an
exponentially small rate, and a sufficiently large time, even extraordinarily
long, has to be allowed for the mixing to take place at small energies. The
equilibrium one particle density function is computed by maximizing the
entropy, and returns an analytical insight into the scrutinized phenomena. | Source: | arXiv, 1505.1734 | Services: | Forum | Review | PDF | Favorites |
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