997 research outputs found
Critical Conductance of a Mesoscopic System: Interplay of the Spectral and Eigenfunction Correlations at the Metal-Insulator Transition
We study the system-size dependence of the averaged critical conductance
at the Anderson transition. We have: (i) related the correction to the spectral correlations; (ii) expressed
in terms of the quantum return probability; (iii) argued that
-- the critical exponent of eigenfunction correlations. Experimental
implications are discussed.Comment: minor changes, to be published in PR
Spin Freezing in Geometrically Frustrated Antiferromagnets with Weak Disorder
We investigate the consequences for geometrically frustrated antiferromagnets
of weak disorder in the strength of exchange interactions. Taking as a model
the classical Heisenberg antiferromagnet with nearest neighbour exchange on the
pyrochlore lattice, we examine low-temperature behaviour. We show that random
exchange generates long-range effective interactions within the extensively
degenerate ground states of the clean system. Using Monte Carlo simulations, we
find a spin glass transition at a temperature set by the disorder strength.
Disorder of this type, which is generated by random strains in the presence of
magnetoelastic coupling, may account for the spin freezing observed in many
geometrically frustrated magnets.Comment: 4 pages, 5 figure
A Note on Wetting Transition for Gradient Fields
We prove existence of a wetting transition for two types of gradient fields:
1) Continuous SOS models in any dimension and 2) Massless Gaussian model in two
dimensions. Combined with a recent result showing the absence of such a
transition for Gaussian models above two dimensions by Bolthausen et al, this
shows in particular that absolute-value and quadratic interactions can give
rise to completely different behaviors.Comment: 6 pages, latex2
Emergent Symmetry at the N\'eel to Valence-Bond-Solid Transition
We show numerically that the `deconfined' quantum critical point between the
N\'eel antiferromagnet and the columnar valence-bond-solid, for a square
lattice of spin-1/2s, has an emergent symmetry. This symmetry allows
the N\'eel vector and the valence-bond-solid order parameter to be rotated into
each other. It is a remarkable 2+1-dimensional analogue of the symmetry that appears in the scaling limit for the
spin-1/2 Heisenberg chain. The emergent is strong evidence that the
phase transition in the 2+1D system is truly continuous, despite the violations
of finite-size scaling observed previously in this problem. It also implies
surprising relations between correlation functions at the transition. The
symmetry enhancement is expected to apply generally to the critical
two-component Abelian Higgs model (non-compact model). The result
indicates that in three dimensions there is an -symmetric conformal
field theory which has no relevant singlet operators, so is radically different
to conventional Wilson-Fisher-type conformal field theories.Comment: 4+epsilon pages, 6 figure
Magnetic charge and ordering in kagome spin ice
We present a numerical study of magnetic ordering in spin ice on kagome, a
two-dimensional lattice of corner-sharing triangles. The magnet has six ground
states and the ordering occurs in two stages, as one might expect for a
six-state clock model. In spin ice with short-range interactions up to second
neighbors, there is an intermediate critical phase separated from the
paramagnetic and ordered phases by Kosterlitz-Thouless transitions. In dipolar
spin ice, the intermediate phase has long-range order of staggered magnetic
charges. The high and low-temperature phase transitions are of the Ising and
3-state Potts universality classes, respectively. Freeze-out of defects in the
charge order produces a very large spin correlation length in the intermediate
phase. As a result of that, the lower-temperature transition appears to be of
the Kosterlitz-Thouless type.Comment: 20 pages, 12 figures, accepted version with minor change
Length Distributions in Loop Soups
Statistical lattice ensembles of loops in three or more dimensions typically
have phases in which the longest loops fill a finite fraction of the system. In
such phases it is natural to ask about the distribution of loop lengths. We
show how to calculate moments of these distributions using or
and O(n) models together with replica techniques. The
resulting joint length distribution for macroscopic loops is Poisson-Dirichlet
with a parameter fixed by the loop fugacity and by symmetries of the
ensemble. We also discuss features of the length distribution for shorter
loops, and use numerical simulations to test and illustrate our conclusions.Comment: 4.5 page
Deconfined Quantum Criticality, Scaling Violations, and Classical Loop Models
Numerical studies of the N\'eel to valence-bond solid phase transition in 2D
quantum antiferromagnets give strong evidence for the remarkable scenario of
deconfined criticality, but display strong violations of finite-size scaling
that are not yet understood. We show how to realise the universal physics of
the Neel-VBS transition in a 3D classical loop model (this includes the
interference effect that suppresses N\'eel hedgehogs). We use this model to
simulate unprecedentedly large systems (of size ). Our results are
compatible with a direct continuous transition at which both order parameters
are critical, and we do not see conventional signs of first-order behaviour.
However, we find that the scaling violations are stronger than previously
realised and are incompatible with conventional finite-size scaling over the
size range studied, even if allowance is made for a weakly/marginally
irrelevant scaling variable. In particular, different determinations of the
anomalous dimensions and yield very
different results. The assumption of conventional finite-size scaling gives
estimates which drift to negative values at large , in violation of
unitarity bounds. In contrast, the behaviour of correlators on scales much
smaller than is consistent with large positive anomalous dimensions.
Barring an unexpected reversal in behaviour at still larger sizes, this implies
that the transition, if continuous, must show unconventional finite-size
scaling, e.g. from a dangerously irrelevant scaling variable. Another
possibility is an anomalously weak first-order transition. By analysing the
renormalisation group flows for the non-compact model (-component
Abelian Higgs model) between two and four dimensions, we give the simplest
scenario by which an anomalously weak first-order transition can arise without
fine-tuning of the Hamiltonian.Comment: 20 pages, 19 figure
Field evolution of the magnetic structures in ErTiO through the critical point
We have measured neutron diffraction patterns in a single crystal sample of
the pyrochlore compound ErTiO in the antiferromagnetic phase
(T=0.3\,K), as a function of the magnetic field, up to 6\,T, applied along the
[110] direction. We determine all the characteristics of the magnetic structure
throughout the quantum critical point at =2\,T. As a main result, all Er
moments align along the field at and their values reach a minimum. Using
a four-sublattice self-consistent calculation, we show that the evolution of
the magnetic structure and the value of the critical field are rather well
reproduced using the same anisotropic exchange tensor as that accounting for
the local paramagnetic susceptibility. In contrast, an isotropic exchange
tensor does not match the moment variations through the critical point. The
model also accounts semi-quantitatively for other experimental data previously
measured, such as the field dependence of the heat capacity, energy of the
dispersionless inelastic modes and transition temperature.Comment: 7 pages; 8 figure
3D loop models and the CP^{n-1} sigma model
Many statistical mechanics problems can be framed in terms of random curves;
we consider a class of three-dimensional loop models that are prototypes for
such ensembles. The models show transitions between phases with infinite loops
and short-loop phases. We map them to sigma models, where is the
loop fugacity. Using Monte Carlo simulations, we find continuous transitions
for , and first order transitions for . The results are
relevant to line defects in random media, as well as to Anderson localization
and -dimensional quantum magnets.Comment: Published versio
Spin Dynamics in Pyrochlore Heisenberg Antiferromagnets
We study the low temperature dynamics of the classical Heisenberg
antiferromagnet with nearest neighbour interactions on the pyrochlore lattice.
We present extensive results for the wavevector and frequency dependence of the
dynamical structure factor, obtained from simulations of the precessional
dynamics. We also construct a solvable stochastic model for dynamics with
conserved magnetisation, which accurately reproduces most features of the
precessional results. Spin correlations relax at a rate independent of
wavevector and proportional to temperature.Comment: 4 pages, 4 figures, submitted to PR
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