250 research outputs found
Symmetric generation of Coxeter groups
We provide involutory symmetric generating sets of finitely generated Coxeter
groups, fulfilling a suitable finiteness condition, which in particular is
fulfilled in the finite, affine and compact hyperbolic cases.Comment: 11 pages, 11 figure
Spin glass transition in a magnetic field: a renormalization group study
We study the transition of short range Ising spin glasses in a magnetic
field, within a general replica symmetric field theory, which contains three
masses and eight cubic couplings, that is defined in terms of the fields
representing the replicon, anomalous and longitudinal modes. We discuss the
symmetry of the theory in the limit of replica number n to 0, and consider the
regular case where the longitudinal and anomalous masses remain degenerate.
The spin glass transitions in zero and non-zero field are analyzed in a
common framework. The mean field treatment shows the usual results, that is a
transition in zero field, where all the modes become critical, and a transition
in non-zero field, at the de Almeida-Thouless (AT) line, with only the replicon
mode critical. Renormalization group methods are used to study the critical
behavior, to order epsilon = 6-d. In the general theory we find a stable
fixed-point associated to the spin glass transition in zero field. This
fixed-point becomes unstable in the presence of a small magnetic field, and we
calculate crossover exponents, which we relate to zero-field critical
exponents. In a finite magnetic field, we find no physical stable fixed-point
to describe the AT transition, in agreement with previous results of other
authors.Comment: 36 pages with 4 tables. To be published in Phys. Rev.
Fast coarsening in unstable epitaxy with desorption
Homoepitaxial growth is unstable towards the formation of pyramidal mounds
when interlayer transport is reduced due to activation barriers to hopping at
step edges. Simulations of a lattice model and a continuum equation show that a
small amount of desorption dramatically speeds up the coarsening of the mound
array, leading to coarsening exponents between 1/3 and 1/2. The underlying
mechanism is the faster growth of larger mounds due to their lower evaporation
rate.Comment: 4 pages, 4 PostScript figure
Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
We examine the spin- quantum Heisenberg magnet with Gaussian-random,
infinite-range exchange interactions. The quantum-disordered phase is accessed
by generalizing to symmetry and studying the large limit. For large
the ground state is a spin-glass, while quantum fluctuations produce a
spin-fluid state for small . The spin-fluid phase is found to be generically
gapless - the average, zero temperature, local dynamic spin-susceptibility
obeys \bar{\chi} (\omega ) \sim \log(1/|\omega|) + i (\pi/2) \mbox{sgn}
(\omega) at low frequencies. This form is identical to the phenomenological
`marginal' spectrum proposed by Varma {\em et. al.\/} for the doped cuprates.Comment: 13 pages, REVTEX, 2 figures available by request from
[email protected]
Coarsening of Surface Structures in Unstable Epitaxial Growth
We study unstable epitaxy on singular surfaces using continuum equations with
a prescribed slope-dependent surface current. We derive scaling relations for
the late stage of growth, where power law coarsening of the mound morphology is
observed. For the lateral size of mounds we obtain with . An analytic treatment within a self-consistent mean-field
approximation predicts multiscaling of the height-height correlation function,
while the direct numerical solution of the continuum equation shows
conventional scaling with z=4, independent of the shape of the surface current.Comment: 15 pages, Latex. Submitted to PR
Fluctuation-dissipation relations in the non-equilibrium critical dynamics of Ising models
We investigate the relation between two-time, multi-spin, correlation and
response functions in the non-equilibrium critical dynamics of Ising models in
d=1 and d=2 spatial dimensions. In these non-equilibrium situations, the
fluctuation-dissipation theorem (FDT) is not satisfied. We find FDT
`violations' qualitatively similar to those reported in various glassy
materials, but quantitatively dependent on the chosen observable, in contrast
to the results obtained in infinite-range glass models. Nevertheless, all FDT
violations can be understood by considering separately the contributions from
large wavevectors, which are at quasi-equilibrium and obey FDT, and from small
wavevectors where a generalized FDT holds with a non-trivial limit
fluctuation-dissipation ratio X. In d=1, we get X = 1/2 for spin observables,
which measure the orientation of domains, while X = 0 for observables that are
sensitive to the domain-wall motion. Numerical simulations in d=2 reveal a
unique X = 0.34 for all observables. Measurement protocols for X are discussed
in detail. Our results suggest that the definition of an effective temperature
Teff = T / X for large length scales is generically possible in non-equilibrium
critical dynamics.Comment: 26 pages, 10 figure
Three-dimensional lattice-Boltzmann simulations of critical spinodal decomposition in binary immiscible fluids
We use a modified Shan-Chen, noiseless lattice-BGK model for binary
immiscible, incompressible, athermal fluids in three dimensions to simulate the
coarsening of domains following a deep quench below the spinodal point from a
symmetric and homogeneous mixture into a two-phase configuration. We find the
average domain size growing with time as , where increases
in the range , consistent with a crossover between
diffusive and hydrodynamic viscous, , behaviour. We find
good collapse onto a single scaling function, yet the domain growth exponents
differ from others' works' for similar values of the unique characteristic
length and time that can be constructed out of the fluid's parameters. This
rebuts claims of universality for the dynamical scaling hypothesis. At early
times, we also find a crossover from to in the scaled structure
function, which disappears when the dynamical scaling reasonably improves at
later times. This excludes noise as the cause for a behaviour, as
proposed by others. We also observe exponential temporal growth of the
structure function during the initial stages of the dynamics and for
wavenumbers less than a threshold value.Comment: 45 pages, 18 figures. Accepted for publication in Physical Review
Competing orders in a magnetic field: spin and charge order in the cuprate superconductors
We describe two-dimensional quantum spin fluctuations in a superconducting
Abrikosov flux lattice induced by a magnetic field applied to a doped Mott
insulator. Complete numerical solutions of a self-consistent large N theory
provide detailed information on the phase diagram and on the spatial structure
of the dynamic spin spectrum. Our results apply to phases with and without
long-range spin density wave order and to the magnetic quantum critical point
separating these phases. We discuss the relationship of our results to a number
of recent neutron scattering measurements on the cuprate superconductors in the
presence of an applied field. We compute the pinning of static charge order by
the vortex cores in the `spin gap' phase where the spin order remains
dynamically fluctuating, and argue that these results apply to recent scanning
tunnelling microscopy (STM) measurements. We show that with a single typical
set of values for the coupling constants, our model describes the field
dependence of the elastic neutron scattering intensities, the absence of
satellite Bragg peaks associated with the vortex lattice in existing neutron
scattering observations, and the spatial extent of charge order in STM
observations. We mention implications of our theory for NMR experiments. We
also present a theoretical discussion of more exotic states that can be built
out of the spin and charge order parameters, including spin nematics and phases
with `exciton fractionalization'.Comment: 36 pages, 33 figures; for a popular introduction, see
http://onsager.physics.yale.edu/superflow.html; (v2) Added reference to new
work of Chen and Ting; (v3) reorganized presentation for improved clarity,
and added new appendix on microscopic origin; (v4) final published version
with minor change
Determination of the Deep Inelastic Contribution to the Generalised Gerasimov-Drell-Hearn Integral for the Proton and Neutron
The virtual photon absorption cross section differences [sigma_1/2-sigma_3/2]
for the proton and neutron have been determined from measurements of polarised
cross section asymmetries in deep inelastic scattering of 27.5 GeV
longitudinally polarised positrons from polarised 1H and 3He internal gas
targets. The data were collected in the region above the nucleon resonances in
the kinematic range nu < 23.5 GeV and 0.8 GeV**2 < Q**2 < 12 GeV**2. For the
proton the contribution to the generalised Gerasimov-Drell-Hearn integral was
found to be substantial and must be included for an accurate determination of
the full integral. Furthermore the data are consistent with a QCD
next-to-leading order fit based on previous deep inelastic scattering data.
Therefore higher twist effects do not appear significant.Comment: 6 pages, 3 figures, 1 table, revte
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