949 research outputs found
Global fluctuations and Gumbel statistics
We explain how the statistics of global observables in correlated systems can
be related to extreme value problems and to Gumbel statistics. This
relationship then naturally leads to the emergence of the generalized Gumbel
distribution G_a(x), with a real index a, in the study of global fluctuations.
To illustrate these findings, we introduce an exactly solvable nonequilibrium
model describing an energy flux on a lattice, with local dissipation, in which
the fluctuations of the global energy are precisely described by the
generalized Gumbel distribution.Comment: 4 pages, 3 figures; final version with minor change
Order by disorder and gauge-like degeneracy in quantum pyrochlore antiferromagnet
The (three-dimensional) pyrochlore lattice antiferromagnet with Heisenberg
spins of large spin length is a highly frustrated model with an macroscopic
degeneracy of classical ground states. The zero-point energy of (harmonic
order) spin wave fluctuations distinguishes a subset of these states. I derive
an approximate but illuminating {\it effective Hamiltonian}, acting within the
subspace of Ising spin configurations representing the {\it collinear} ground
states. It consists of products of Ising spins around loops, i.e has the form
of a lattice gauge theory. The remaining ground state entropy is still
infinite but not extensive, being for system size . All these
ground states have unit cells bigger than those considered previously.Comment: 4pp, one figur
Dipolar interaction and incoherent quantum tunneling: a Monte Carlo study of magnetic relaxation
We study the magnetic relaxation of a system of localized spins interacting
through weak dipole interactions, at a temperature large with respect to the
ordering temperature but low with respect to the crystal field level splitting.
The relaxation results from quantum spin tunneling but is only allowed on sites
where the dipole field is very small. At low times, the magnetization decrease
is proportional to as predicted by Prokofiev and Stamp, and at long
times the relaxation can be described as an extension of a relaxed zone. The
results can be directly compared with very recent experimental data on Fe_8
molecular clusters.Comment: 9 pages, 11 figures; accepted for publication on Eur. Phys. J.
Effects of semiclassical spiral fluctuations on hole dynamics
We investigate the dynamics of a single hole coupled to the spiral
fluctuations related to the magnetic ground states of the antiferromagnetic
J_1-J_2-J_3 Heisenberg model on a square lattice. Using exact diagonalization
on finite size clusters and the self consistent Born approximation in the
thermodynamic limit we find, as a general feature, a strong reduction of the
quasiparticle weight along the spiral phases of the magnetic phase diagram. For
an important region of the Brillouin Zone the hole spectral functions are
completely incoherent, whereas at low energies the spectral weight is
redistributed on several irregular peaks. We find a characteristic value of the
spiral pitch, Q=(0.7,0.7)\pi, for which the available phase space for hole
scattering is maximum. We argue that this behavior is due to the non trivial
interference of the magnon assisted and the free hopping mechanism for hole
motion, characteristic of a hole coupled to semiclassical spiral fluctuations.Comment: 6 pages, 5 figure
Conserved Growth on Vicinal Surfaces
A crystal surface which is miscut with respect to a high symmetry plane
exhibits steps with a characteristic distance. It is argued that the continuum
description of growth on such a surface, when desorption can be neglected, is
given by the anisotropic version of the conserved KPZ equation (T. Sun, H. Guo,
and M. Grant, Phys. Rev. A 40, 6763 (1989)) with non-conserved noise. A
one--loop dynamical renormalization group calculation yields the values of the
dynamical exponent and the roughness exponent which are shown to be the same as
in the isotropic case. The results presented here should apply in particular to
growth under conditions which are typical for molecular beam epitaxy.Comment: 10 pages, uses revte
Surface currents and slope selection in crystal growth
We face the problem to determine the slope dependent current during the
epitaxial growth process of a crystal surface. This current is proportional to
delta=(p+) + (p-), where (p+/-) are the probabilities for an atom landing on a
terrace to attach to the ascending (p+) or descending (p-) step. If the landing
probability is spatially uniform, the current is proved to be proportional to
the average (signed) distance traveled by an adatom before incorporation in the
growing surface. The phenomenon of slope selection is determined by the
vanishing of the asymmetry delta. We apply our results to the case of atoms
feeling step edge barriers and downward funnelling, or step edge barriers and
steering. In the general case, it is not correct to consider the slope
dependent current j as a sum of separate contributions due to different
mechanisms.Comment: 6 pages. The text has been strongly revised and Fig.1 has been
changed. Accepted for publication in the "Comptes Rendus Physique
Phonon superradiance and phonon laser effect in nanomagnets
We show that the theory of spin-phonon processes in paramagnetic solids must
take into account the coherent generation of phonons by the magnetic centers.
This effect should drastically enhance spin-phonon rates in nanoscale
paramagnets and in crystals of molecular nanomagnets.Comment: 4 PR pages, 1 Figur
Simplex solid states of SU(N) quantum antiferromagnets
I define a set of wavefunctions for SU(N) lattice antiferromagnets, analogous
to the valence bond solid states of Affleck, Kennedy, Lieb, and Tasaki (AKLT),
in which the singlets are extended over N-site simplices. As with the valence
bond solids, the new simplex solid (SS) states are extinguished by certain
local projection operators, allowing us to construct Hamiltonians with local
interactions which render the SS states exact ground states. Using a coherent
state representation, we show that the quantum correlations in each SS state
are calculable as the finite temperature correlations of an associated
classical model, with N-spin interactions, on the same lattice. In three and
higher dimensions, the SS states can spontaneously break SU(N) and exhibit
N-sublattice long-ranged order, as a function of a discrete parameter which
fixes the local representation of SU(N). I analyze this transition using a
classical mean field approach. For N>2 the ordered state is selected via an
"order by disorder" mechanism. As in the AKLT case, the bulk representations
fractionalize at an edge, and the ground state entropy is proportional to the
volume of the boundary.Comment: 14 pages, 8 figures, minor typos correcte
Monte Carlo study of the two-dimensional site-diluted dipolar Ising model
By tempered Monte Carlo simulations, we study 2D site-diluted dipolar Ising
systems. Dipoles are randomly placed on a fraction x of all L^2 sites in a
square lattice, and point along a common crystalline axis. For x_c< x<=1, where
x_c = 0.79(5), we find an antiferromagnetic phase below a temperature which
vanishes as x approaches x_c from above. At lower values of x, we study (i)
distributions of the spin--glass (SG) overlap q, (ii) their relative mean
square deviation Delta_q^2 and kurtosis and (iii) xi_L/L, where xi_L is a SG
correlation length. From their variation with temperature and system size, we
find that the paramagnetic phase covers the entire T>0 range. Our results
enable us to obtain an estimate of the critical exponent associated to the
correlation length at T=0, 1/nu=0.35(10).Comment: 10 LaTeX pages, 10 figures, 1 table
Lattice gas description of pyrochlore and checkerboard antiferromagnets in a strong magnetic field
Quantum Heisenberg antiferromagnets on pyrochlore and checkerboard lattices
in a strong external magnetic field are mapped onto hard-core lattice gases
with an extended exclusion region. The effective models are studied by the
exchange Monte Carlo simulations and by the transfer matrix method. The
transition point and the critical exponents are obtained numerically for a
square-lattice gas of particles with the second-neighbor exclusion, which
describes a checkerboard antiferromagnet. The exact structure of the magnon
crystal state is determined for a pyrochlore antiferromagnet.Comment: 11 pages, accepted versio
- …