11,530 research outputs found
Numerical revision of the universal amplitude ratios for the two-dimensional 4-state Potts model
Monte Carlo (MC) simulations and series expansion (SE) data for the energy,
specific heat, magnetization and susceptibility of the ferromagnetic 4-state
Potts model on the square lattice are analyzed in a vicinity of the critical
point in order to estimate universal combinations of critical amplitudes. The
quality of the fits is improved using predictions of the renormalization group
(RG) approach and of conformal invariance, and restricting the data within an
appropriate temperature window.
The RG predictions on the cancelation of the logarithmic corrections in the
universal amplitude ratios are tested. A direct calculation of the effective
ratio of the energy amplitudes using duality relations explicitly demonstrates
this cancelation of logarithms, thus supporting the predictions of RG.
We emphasize the role of corrections of background terms on the determination
of the amplitudes. The ratios of the critical amplitudes of the
susceptibilities obtained in our analysis differ significantly from those
predicted theoretically and supported by earlier SE and MC analysis. This
disagreement might signal that the two-kink approximation used in the
analytical estimates is not sufficient to describe with fair accuracy the
amplitudes of the 4-state model.Comment: 32 pages, 9 figures, 11 table
Entanglement Entropy and Full Counting Statistics for -Rotating Trapped Fermions
We consider non-interacting fermions in a harmonic potential of
trapping frequency and in a rotating frame at angular frequency
, with . At zero temperature, the fermions
are in the non-degenerate lowest Landau level and their positions are in one to
one correspondence with the eigenvalues of an complex Ginibre
matrix. For large , the fermion density is uniform over the disk of radius
centered at the origin and vanishes outside this disk. We compute
exactly, for any finite , the R\'enyi entanglement entropy of order ,
, as well as the cumulants of order , ,
of the number of fermions in a disk of radius centered at the origin.
For , in the (extended) bulk, i.e., for , we show
that is proportional to the number variance ,
despite the non-Gaussian fluctuations of . This relation breaks down at
the edge of the fermion density, for , where we show
analytically that and have a different
-dependence.Comment: 6 pages + 7 pages (Supplementary material), 2 Figure
Extremes of Coulomb gas: universal intermediate deviation regime
In this paper, we study the extreme statistics in the complex Ginibre
ensemble of random matrices with complex Gaussian entries, but
with no other symmetries. All the eigenvalues are complex random variables
and their joint distribution can be interpreted as a Coulomb gas with a
logarithmic repulsion between any pair of particles and in presence of a
confining harmonic potential . We study the statistics of the
eigenvalue with the largest modulus in the complex plane. The
typical and large fluctuations of around its mean had been studied
before, and they match smoothly to the right of the mean. However, it remained
a puzzle to understand why the large and typical fluctuations to the left of
the mean did not match. In this paper, we show that there is indeed an
intermediate fluctuation regime that interpolates smoothly between the large
and the typical fluctuations to the left of the mean. Moreover, we compute
explicitly this "intermediate deviation function" (IDF) and show that it is
universal, i.e. independent of the confining potential as long as it is
spherically symmetric and increases faster than for large with an
unbounded support. If the confining potential has a finite support, i.e.
becomes infinite beyond a finite radius, we show via explicit computation that
the corresponding IDF is different. Interestingly, in the borderline case where
the confining potential grows very slowly as for
with an unbounded support, the intermediate regime disappears and there is a
smooth matching between the central part and the left large deviation regime.Comment: 36 pages, 7 figure
Using torsion to manipulate spin currents
We address the problem of quantum particles moving on a manifold
characterised by the presence of torsion along a preferential axis. In fact,
such a torsion may be taylored by the presence of a single screw dislocation,
whose Burgers vector measures the torsion amplitude. The problem, first treated
in the relativistic limit describing fermions that couple minimally to torsion,
is then analysed in the Pauli limit We show that torsion induces a geometric
potential and also that it couples generically to the phase of the wave
function, giving rise to the possibility of using torsion to manipulate spin
currents in the case of spinor wave functions. These results emerge as an
alternative strategy for using screw dislocations in the design of
spintronic-based devices
Introduction. Intégration des enjeux environnementaux dans la gestion du foncier agricole
Ce numéro consacré à la gestion du foncier agricole et à l'intégration des enjeux environnementaux apporte trois éclairages sur la base de contributions de chercheurs de disciplines différentes, et de témoignages d'acteurs de terrain qui dans leur quotidien, en tant que techniciens, élus, gestionnaires, sont partie prenante de la gouvernance foncière des espaces agricoles. Le premier concerne la construction sociale de l'enjeu environnemental et des réponses territoriales qui sont apportées. Le second axe de réflexion examine les espaces métropolitains comme de nouvelles échelles de gouvernance foncière agricole et environnementale. Le troisième et dernier axe de réflexion sur l'intégration des enjeux environnementaux dans la gestion du foncier agricole s'attache aux innovations en matière de gouvernance et de pratiques qui émergent aujourd'hui à l'échelle des territoires
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