714 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
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
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
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
Intergenerational linkages in consumption patterns and the geographical distribution of surnames
We specially thank Luis Ubeda for his very useful suggestions and comments. We
also thank Klaus Desmet, Jaime Kahhat, Javier Ruiz-Castillo, Christian Schultz and two
anonymous refereesThis paper attempts to detect the existence of links in consumption patterns between generations. Preferences
over consumption goods may be determined by the preferences of parents and/or by preferences arising from
the environment. We propose an indirect methodology to overcome the lack of data on consumption choices
of dynasties, i.e., parents and their adult offspring. This new approach is based on the analysis of the correlation
between the geographical distributions of surnames and consumption choices.We show that there is no signifi
cant intergenerational link on consumption patterns for non food goods. Our results also suggest that there is a link
between parents' and children's preferences over food itemsAuthors gratefully acknowledge financial support from
the Spanish MEC through grants ECO2008-05721, ECO2011-29751, ECO 2010-19596
and ECO2010-19830. Romeu also acknowledges financial support from Fundación SENECA
11998Publicad
Fluctuations of the correlation dimension at metal-insulator transitions
We investigate numerically the inverse participation ratio, , of the 3D
Anderson model and of the power-law random banded matrix (PRBM) model at
criticality. We found that the variance of scales with system size
as , being the
correlation dimension and the system dimension. Therefore the concept of a
correlation dimension is well defined in the two models considered. The 3D
Anderson transition and the PRBM transition for (see the text for the
definition of ) are fairly similar with respect to all critical magnitudes
studied.Comment: RevTex, 5 pages, 4 eps figures, to be published in Phys. Rev. Let
Crossover from diffusive to strongly localized regime in two-dimensional systems
We have studied the conductance distribution function of two-dimensional
disordered noninteracting systems in the crossover regime between the diffusive
and the localized phases. The distribution is entirely determined by the mean
conductance, g, in agreement with the strong version of the single-parameter
scaling hypothesis. The distribution seems to change drastically at a critical
value very close to one. For conductances larger than this critical value, the
distribution is roughly Gaussian while for smaller values it resembles a
log-normal distribution. The two distributions match at the critical point with
an often appreciable change in behavior. This matching implies a jump in the
first derivative of the distribution which does not seem to disappear as system
size increases. We have also studied 1/g corrections to the skewness to
quantify the deviation of the distribution from a Gaussian function in the
diffusive regime.Comment: 4 pages, 4 figure
- …