374 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
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
Random Walks and Anderson Localisation in a Three-Dimensional Class C Network Model
We study the disorder-induced localisation transition in a three-dimensional
network model that belongs to symmetry class C. The model represents
quasiparticle dynamics in a gapless spin-singlet superconductor without
time-reversal invariance. It is a special feature of network models with this
symmetry that the conductance and density of states can be expressed as
averages in a classical system of dense, interacting random walks. Using this
mapping, we present a more precise numerical study of critical behaviour at an
Anderson transition than has been possible previously in any context
Demonstration experiments for solid state physics using a table top mechanical Stirling refrigerator
Liquid free cryogenic devices are acquiring importance in basic science and
engineering. But they can also lead to improvements in teaching low temperature
an solid state physics to graduate students and specialists. Most of the
devices are relatively expensive, but small sized equipment is slowly becoming
available. Here, we have designed several simple experiments which can be
performed using a small Stirling refrigerator. We discuss the measurement of
the critical current and temperature of a bulk YBa2Cu3O(7-d) (YBCO) sample, the
observation of the levitation of a magnet over a YBCO disk when cooled below
the critical temperature and the observation of a phase transition using ac
calorimetry. The equipment can be easily handled by students, and also used to
teach the principles of liquid free cooling
Spin quantum Hall effect and plateau transitions in multilayer network models
We study the spin quantum Hall effect and transitions between Hall plateaus
in quasi two-dimensional network models consisting of several coupled layers.
Systems exhibiting the spin quantum Hall effect belong to class C in the
symmetry classification for Anderson localisation, and for network models in
this class there is an established mapping between the quantum problem and a
classical one involving random walks. This mapping permits numerical studies of
plateau transitions in much larger samples than for other symmetry classes, and
we use it to examine localisation in systems consisting of weakly coupled
layers. Standard scaling ideas lead one to expect distinct plateau
transitions, but in the case of the unitary symmetry class this conclusion has
been questioned. Focussing on a two-layer model, we demonstrate that there are
two separate plateau transitions, with the same critical properties as in a
single-layer model, even for very weak interlayer coupling.Comment: 5 pages, 6 figure
A new mixed-integer programming model for irregular strip packing based on vertical slices with a reproducible survey
The irregular strip-packing problem, also known as nesting or marker making, is defined as the automatic computation of a non-overlapping placement of a set of non-convex polygons onto a rectangular strip of fixed width and unbounded length, such that the strip length is minimized. Nesting methods based on heuristics are a mature technology, and currently, the only practical solution to this problem. However, recent performance gains of the Mixed-Integer Programming (MIP) solvers, together with the known limitations of the heuristics methods, have encouraged the exploration of exact optimization models for nesting during the last decade. Despite the research effort, the current family of exact MIP models for nesting cannot efficiently solve both large problem instances and instances containing polygons with complex geometries. In order to improve the efficiency of the current MIP models, this work introduces a new family of continuous MIP models based on a novel formulation of the NoFit-Polygon Covering Model (NFP-CM), called NFP-CM based on Vertical Slices (NFP-CM-VS). Our new family of MIP models is based on a new convex decomposition of the feasible space of relative placements between pieces into vertical slices, together with a new family of valid inequalities, symmetry breakings, and variable eliminations derived from the former convex decomposition. Our experiments show that our new NFP-CM-VS models outperform the current state-of-the-art MIP models. Finally, we provide a detailed reproducibility protocol and dataset based on our Java software library as supplementary material to allow the exact replication of our models, experiments, and results
On modelling planning under uncertainty in manufacturing
We present a modelling framework for two-stage and multi-stage mixed 0-1 problems under uncertainty for strategic Supply Chain Management, tactical production planning and operations assignment and scheduling. A scenario tree based scheme is used to represent the uncertainty. We present the Deterministic Equivalent Model of the stochastic mixed 0-1 programs with complete recourse that we study. The constraints are modelled by compact and splitting variable representations via scenarios
Charge occupancy of two interacting electrons on artificial molecules - exact results
We present exact solutions for two interacting electrons on an artificial
atom and on an artificial molecule made by one and two (single level) quantum
dots connected by ideal leads. Specifically, we calculate the accumulated
charge on the dots as function of the gate voltage, for various strengths of
the electron-electron interaction and of the hybridization between the dots and
the (one-dimensional) leads. With increasing of the (negative) gate voltage,
the accumulated charge in the two-electron ground state increases in gradual
steps from 0 to 1 and then to 2. The value 0 represents an "insulating" state,
where both electrons are bound to shallow states on the impurities. The value
of 1 corresponds to a "metal", with one electron localized on the dots and the
other extended on the leads. The value of 2 corresponds to another "insulator",
with both electrons strongly localized. The width of the "metallic" regime
diverges with strength of the electron-electron interaction for the single dot,
but remains very narrow for the double dot. These results are contrasted with
the simple Coulomb blockade picture.Comment: 12 pages, 7 figure
A New Ant Colony-Based Methodology for Disaster Relief
Humanitarian logistics in response to large scale disasters entails decisions that must be taken urgently and under high uncertainty. In addition, the scarcity of available resources sometimes causes the involved organizations to suffer assaults while transporting the humanitarian aid. This paper addresses the last mile distribution problem that arises in such an insecure environment, in which vehicles are often forced to travel together forming convoys for security reasons. We develop an elaborated methodology based on Ant Colony Optimization that is applied to two case studies built from real disasters, namely the 2010 Haiti earthquake and the 2005 Niger famine. There are very few works in the literature dealing with problems in this context, and that is the research gap this paper tries to fill. Furthermore, the consideration of multiple criteria such as cost, time, equity, reliability, security or priority, is also an important contribution to the literature, in addition to the use of specialized ants and effective pheromones that are novel elements of the algorithm which could be exported to other similar problems. Computational results illustrate the efficiency of the new methodology, confirming it could be a good basis for a decision support tool for real operations
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