991 research outputs found
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
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
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
Charging of highly resistive granular metal films
We have used the Scanning Kelvin probe microscopy technique to monitor the
charging process of highly resistive granular thin films. The sample is
connected to two leads and is separated by an insulator layer from a gate
electrode. When a gate voltage is applied, charges enter from the leads and
rearrange across the sample. We find very slow processes with characteristic
charging times exponentially distributed over a wide range of values, resulting
in a logarithmic relaxation to equilibrium. After the gate voltage has been
switched off, the system again relaxes logarithmically slowly to the new
equilibrium. The results cannot be explained with diffusion models, but most of
them can be understood with a hopping percolation model, in which the
localization length is shorter than the typical site separation. The technique
is very promising for the study of slow phenomena in highly resistive systems
and will be able to estimate the conductance of these systems when direct
macroscopic measurement techniques are not sensitive enough.Comment: 8 pages, 7 figure
Effects of many-electron jumps in relaxation and conductivity of Coulomb glasses
A numerical study of the energy relaxation and conductivity of the Coulomb
glass is presented. The role of many-electron transitions is studied by two
complementary methods: a kinetic Monte Carlo algorithm and a master equation in
configuration space method. A calculation of the transition rate for
two-electron transitions is presented, and the proper extension of this to
multi-electron transitions is discussed. It is shown that two-electron
transitions are important in bypassing energy barriers which effectively block
sequential one-electron transitions. The effect of two-electron transitions is
also discussed.Comment: 8 pages, 6 figure
A stochastic frontier analysis approach for estimating energy demand and efficiency in the transport sector of Latin America and the Caribbean
In this paper, a stochastic frontier analysis approach is applied to estimate energy demand functions in the transport sector. This approach allows us to obtain energy efficiency measures at country level that are a robust alternative to the energy intensity indicators commonly used for international comparisons. A transitive multilateral price index is constructed for aggregating the diverse energy components employed in the sector. Due to the likely unobserved heterogeneity among countries, the use of a random parameters model is proposed to accommodate these differences and to obtain different income and price elasticities per country. The estimated model is compared with alternative approaches of addressing this issue such as latent class, true fixed effects or true random effects models. This study is the first to use a random parameters stochastic frontier approach in the estimation of energy demand functions. The proposed procedure is applied to Latin America and the Caribbean, where the transport sector represents a large share of total energy consumption
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