Phase diagrams of one-, two-, and three-dimensional quantum spin systems

2016 ◽  
Vol 16 (9&10) ◽  
pp. 885-899
Author(s):  
Briiissuurs Braiorr-Orrs ◽  
Michael Weyrauch ◽  
Mykhailo V. Rakov
Keyword(s):  
Three Dimensional ◽  
Transverse Field ◽  
Quantum Spin ◽  
Three Dimensions ◽  
Quantum Spin Systems ◽  
Bipartite Entanglement ◽  
Spatial Dimensions ◽  
Characteristic Features ◽  
Quantum Spin Models ◽  
2D And 3D

We study the bipartite entanglement per bond to determine characteristic features of the phase diagram of various quantum spin models in different spatial dimensions. The bipartite entanglement is obtained from a tensor network representation of the ground state wave-function. Three spin-1/2 models (Ising, XY, XXZ, all in a transverse field) are investigated. Infinite imaginary-time evolution (iTEBD in 1D, ‘simple update’ in 2D and 3D) is used to determine the ground states of these models. The phase structure of the models is discussed for all three dimensions.

scholarly journals General Method for Extending Discrete Global Grid Systems to Three Dimensions

2020 ◽  
Vol 9 (4) ◽  
pp. 233 ◽  
Author(s):  
Benjamin Ulmer ◽  
John Hall ◽  
Faramarz Samavati
Keyword(s):  
Three Dimensional ◽  
Use Cases ◽  
Three Dimensions ◽  
Grid Systems ◽  
3D Data ◽  
Third Dimension ◽  
2D And 3D ◽  
Polyhedral Projection ◽  
Global Grid ◽  
General Method

Geospatial sensors are generating increasing amounts of three-dimensional (3D) data. While Discrete Global Grid Systems (DGGS) are a useful tool for integrating geospatial data, they provide no native support for 3D data. Several different 3D global grids have been proposed; however, these approaches are not consistent with state-of-the-art DGGSs. In this paper, we propose a general method that can extend any DGGS to the third dimension to operate as a 3D DGGS. This extension is done carefully to ensure any valid DGGS can be supported, including all refinement factors and non-congruent refinement. We define encoding, decoding, and indexing operations in a way that splits responsibility between the surface DGGS and the 3D component, which allows for easy transference of data between the 2D and 3D versions of a DGGS. As a part of this, we use radial mapping functions that serve a similar purpose as polyhedral projection in a conventional DGGS. We validate our method by creating three different 3D DGGSs tailored for three specific use cases. These use cases demonstrate our ability to quickly generate 3D global grids while achieving desired properties such as support for large ranges of altitudes, volume preservation between cells, and custom cell aspect ratio.

scholarly journals Gold Exploration in Two and Three Dimensions: Improved and Correlative Insights from Microscopy and X-Ray Computed Tomography

Minerals ◽  
2020 ◽  
Vol 10 (5) ◽  
pp. 476
Author(s):  
Joshua Chisambi ◽  
Bjorn von der Heyden ◽  
Muofhe Tshibalanganda ◽  
Stephan Le Roux
Keyword(s):  
Computed Tomography ◽  
Spatial Distribution ◽  
Gold Mineralization ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Low Grade ◽  
X Ray ◽  
3D Space ◽  
X Ray Computed ◽  
2D And 3D

In this contribution, we highlight a correlative approach in which three-dimensional structural/positional data are combined with two dimensional chemical and mineralogical data to understand a complex orogenic gold mineralization system; we use the Kirk Range (southern Malawi) as a case study. Three dimensional structures and semi-quantitative mineral distributions were evaluated using X-ray Computed Tomography (XCT) and this was augmented with textural, mineralogical and chemical imaging using Scanning Electron Microscopy (SEM) and optical microscopy as well as fire assay. Our results detail the utility of the correlative approach both for quantifying gold concentrations in core samples (which is often nuggety and may thus be misrepresented by quarter- or half-core assays), and for understanding the spatial distribution of gold and associated structures and microstructures in 3D space. This approach overlays complementary datasets from 2D and 3D analytical protocols, thereby allowing a better and more comprehensive understanding on the distribution and structures controlling gold mineralization. Combining 3D XCT analyses with conventional 2D microscopies derive the full value out of a given exploration drilling program and it provides an excellent tool for understanding gold mineralization. Understanding the spatial distribution of gold and associated structures and microstructures in 3D space holds vast potential for exploration practitioners, especially if the correlative approach can be automated and if the resultant spatially-constrained microstructural information can be fed directly into commercially available geological modelling software. The extra layers of information provided by using correlative 2D and 3D microscopies offer an exciting new tool to enhance and optimize mineral exploration workflows, given that modern exploration efforts are targeting increasingly complex and low-grade ore deposits.

A UNIFIED RENORMALIZATION GROUP STUDY OF THE 1D ISING MODEL WITH TRANSVERSE FIELD

1995 ◽  
Vol 09 (02) ◽  
pp. 103-111
Author(s):  
C. Y. PAN ◽  
H.Q. LIN
Keyword(s):  
Renormalization Group ◽  
Ising Model ◽  
Transverse Field ◽  
Real Space ◽  
Mapping Method ◽  
Quantum Spin ◽  
Quantum Spin Systems ◽  
Real Space Renormalization Group ◽  
Group Methods ◽  
The One

By applying a unified real space renormalization group (URG) mapping method, we study the one-dimensional spin-1/2 Ising model with a transverse field (ITF). Unlike the other real space renormalization group methods, the URG method describes the properties of the model at both zero and finite temperatures in a unified way. The results obtained are in good agreement with that obtained by other methods. Application of the URG method to other quantum spin systems is discussed.

scholarly journals Topological Excitations in Quantum Spin Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Ranjan Chaudhury ◽  
Samir K. Paul
Keyword(s):  
Great Depth ◽  
Quantum Spin ◽  
Spin Fluctuations ◽  
Quantum Spin Systems ◽  
Low Dimensions ◽  
Topological Excitations ◽  
Novel Approach ◽  
Theoretical Predictions ◽  
Quantum Action ◽  
Quantum Spin Models

The origin and significance of topological excitations in quantum spin models in low dimensions are presented in detail. Besides a general review, our own work in this area is described in great depth. Apart from theoretical analysis of the existence and properties of spin vortices and antivortices, the possible experimental consequences and signatures are also highlighted. In particular, the distinguishing features between the even and odd charged topological excitations are brought out through a detailed analysis of the topological term in the quantum action. Moreover, an interesting symmetry property is predicted between the excitations from a ferromagnetic model and an antiferromagnetic model. Through a novel approach of ours, a bridge is established between field theoretical formalism and the well-known statistical mechanical treatment of Berezinskii-Kosterlitz-Thouless (BKT) transition involving these topological excitations. Furthermore, a detailed phenomenological analysis of the experimentally observed static and dynamic magnetic properties of the layered magnetic materials, possessing XY anisotropy in the in-plane spin-spin couplings, is undertaken to test the theoretical predictions regarding the behaviour of these excitations. The importance and the crucial role of quantum spin fluctuations in these studies are also brought out very clearly by our analysis.

Reevaluating Constructivist Norm Theory: A Three-Dimensional Norms Research Program

2022 ◽  
Vol 24 (1) ◽  
Author(s):  
Jeffrey S Lantis ◽  
Carmen Wunderlich
Keyword(s):  
Three Dimensional ◽  
World Politics ◽  
Three Dimensions ◽  
Research Progress ◽  
Three Dimensional Model ◽  
Critical Dimensions ◽  
Complex Processes ◽  
Syrian Civil War ◽  
Spatial Dimensions ◽  
The Face

Abstract Constructivist theories of norm dynamics offer a variety of analytical tools to understand the complex processes of norm emergence, diffusion, and evolution over time. As the literature has developed, though, it lacks a general framing of the interconnections between norms, norm clusters or configurations, and principles or “normativity.” This article advances a new three-dimensional model of constructivist theories of norms that emphasizes the spatial dimensions of norm meanings, legitimacy, and impact and identifies promising avenues for research progress. First, individual norms represent a primary intersubjective structural component that is both developed and contested. Second, theories of norm interrelations or norm clusters provide additional critical dimensions of structuration that may promote resiliency in the face of contestation. Third, norms exist within a larger constellation of norm structures, representing the broadest dimension in world politics. Collisions can occur in this environment, but broader normativity and institutionalization often become activated in the face of serious challenges. As demonstrated using the illustration of international responses to the Syrian civil war (2011 till present), only by attending to all three dimensions of norms can we gain a more accurate understanding of real-world circumstances of norm connections, norm collisions, and the variable effects of norm contestation. The article concludes by identifying promising research avenues building from the three-dimensional framework.

scholarly journals Exploring the physics of core-collapse supernovae with multidimensional simulations: from axisymmetry to three dimensions

2016 ◽  
Vol 12 (S329) ◽  
pp. 449-449
Author(s):  
Alexander Summa ◽  
Hans-Thomas Janka ◽  
Florian Hanke ◽  
Tobias Melson ◽  
Andreas Marek ◽  
...  
Keyword(s):  
Accretion Rate ◽  
Three Dimensional ◽  
Strong Shock ◽  
Three Dimensions ◽  
Core Collapse ◽  
3D Simulations ◽  
Ram Pressure ◽  
Self Consistent ◽  
Spatial Dimensions ◽  
Effects Of Rotation

AbstractMultidimensional effects are essential for the success of the neutrino-driven explosion mechanism of core-collapse supernovae. Although astrophysical phenomena in nature involve three spatial dimensions, the huge computational demands still allow only for a few self-consistent, three-dimensional (3D) simulations focusing on specific aspects of the explosion physics, whereas systematic studies of larger sets of progenitor models or detailed investigations of different explosion parameters are restricted to the axisymmetric (2D) modeling approach at the moment. Employing state-of-the-art neutrino physics, we present the results of self-consistent core-collapse supernova simulations performed with the Prometheus-Vertex code in 2D and 3D. The 2D study of 18 successfully exploding pre-supernova models in the range of 11 to 28 solar masses shows the progenitor dependence of the explosion dynamics: if the progenitor exhibits a pronounced decline of the density at the Si/Si-O composition shell interface, the rapid drop of the mass-accretion rate at the time the interface arrives at the shock induces a steep reduction of the accretion ram pressure. This causes a strong shock expansion supported by neutrino heating and thus favors an early explosion. In case of a more gradually decreasing accretion rate, it takes longer for the neutrino heating to overcome the accretion ram pressure and explosions set in later. By considering the effects of turbulent pressure in the gain layer, we derive a generalized condition for the critical neutrino luminosity that captures the explosion behavior of all models very well. We show that this concept can also be extended to describe the effects of rotation as well as the behavior of recent 3D simulations and that the conditions necessary for the onset of explosion can be defined in a similar way.

Three-dimensional kernel utilization distributions improve estimates of space use in aquatic animals

2012 ◽  
Vol 69 (3) ◽  
pp. 565-572 ◽  
Author(s):  
Colin A. Simpfendorfer ◽  
Esben M. Olsen ◽  
Michelle R. Heupel ◽  
Even Moland
Keyword(s):  
Animal Movement ◽  
Three Dimensional ◽  
Anguilla Anguilla ◽  
Space Use ◽  
Three Dimensions ◽  
Activity Space ◽  
Separate Analysis ◽  
Tracking Data ◽  
Utilization Distributions ◽  
2D And 3D

Tracking data have previously been used to define animal movement patterns through two-dimensional (2D) kernel utilization distributions and separate analysis of vertical locations. Here we describe the use of three-dimensional (3D) kernel utilization distributions to estimate the volumetric space use of individuals based on tracking data and to estimate the overlap in activity space between individuals. Data from European eels ( Anguilla anguilla ) from Norwegian coastal waters were used to compare the information conveyed by 2D and 3D activity space estimates and the utility of this approach for aquatic species. The use of 3D kernels produced detailed representations of space use in A. anguilla that permitted examination of depth use in a geographic context. Comparison of 2D and 3D home ranges showed that 2D analyses overestimated the amount of overlap between individuals by 13%–20%, because individuals sometimes occurred in the same location but used different depths. Hence, the 3D approach provided more comprehensive representations of animal movement in three dimensions while producing a metric that can be used for testing hypotheses relating to scientific descriptions of activity space, habitat use, and movement parameters.

scholarly journals Quaternionic Assessment of EEG Traces on Nervous Multidimensional Hyperspheres

2020 ◽  
Author(s):  
Arturo Tozzi ◽  
James F. Peters ◽  
Norbert Jausovec ◽  
Irina Legchenkova ◽  
Edward Bormashenko
Keyword(s):  
Nervous Activity ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Data Sets ◽  
Operational Procedure ◽  
Higher Dimensional ◽  
Spatial Dimensions ◽  
The Brain ◽  
Real Experimental Data ◽  
Operational Assessment

The nervous activity of the brain takes place in higher-dimensional functional spaces. Indeed, recent claims advocate that the brain might be equipped with a phase space displaying four spatial dimensions plus time, instead of the classical three plus time. This suggests the possibility to investigate global visualization methods for exploiting four-dimensional maps of real experimental data sets. Here we asked whether, starting from the conventional neuro-data available in three dimensions plus time, it is feasible to find an operational procedure to describe the corresponding four-dimensional trajectories. In particular, we used quaternion orthographic projections for the assessment of electroencephalographic traces (EEG) from scalp locations. This approach makes it possible to map three-dimensional EEG traces to the surface of a four-dimensional hypersphere, which has an important advantage, since quaternionic networks make it feasible to enlighten temporally far apart nervous trajectories equipped with the same features, such as the same frequency or amplitude of electric oscillations. This leads to an incisive operational assessment of symmetries, dualities and matching descriptions hidden in the very structure of complex neuro-data signals.

NOVEL PATH INTEGRAL APPROACH TO EFFECTIVE FIELD THEORIES FOR D-DIMENSIONAL QUANTUM SPIN SYSTEMS

1989 ◽  
Vol 03 (07) ◽  
pp. 1069-1083 ◽  
Author(s):  
ANTIMO ANGELUCCI ◽  
GIANCARLO JUG
Keyword(s):  
Path Integral ◽  
Effective Field ◽  
Quantum Spin ◽  
Integral Approach ◽  
Spin Liquid ◽  
Quantum Spin Systems ◽  
New Approach ◽  
Higher Temperature ◽  
Quantum Spin Models ◽  
Quantum Spin Liquid

We present a novel path integral formulation for the effective field theory describing d-dimensional quantum spin models. The new approach avoids the coherent states representation, but at very low temperatures reproduces all known results obtained with the latter technique for describing excitations of the Neél state. The possibility of exploring higher-temperature, unbroken-symmetry state excitations (such as those appropriate for the quantum spin-liquid state) within this method is illustrated.

scholarly journals Three-dimensional simulations of non-resonant streaming instability and particle acceleration near non-relativistic astrophysical shocks

2019 ◽  
Vol 490 (1) ◽  
pp. 1156-1165 ◽  
Author(s):  
Allard Jan van Marle ◽  
Fabien Casse ◽  
Alexandre Marcowith
Keyword(s):  
Magnetic Field ◽  
Particle Acceleration ◽  
Three Dimensional ◽  
3D Models ◽  
Three Dimensions ◽  
Spectral Energy ◽  
Growth Speed ◽  
Field Amplification ◽  
Streaming Instability ◽  
2D And 3D

ABSTRACT We use particle-in-magnetohydrodynamics-cells to model particle acceleration and magnetic field amplification in a high-Mach, parallel shock in three dimensions and compare the result to 2D models. This allows us to determine whether 2D simulations can be relied upon to yield accurate results in terms of particle acceleration, magnetic field amplification, and the growth rate of instabilities. Our simulations show that the behaviour of the gas and the evolution of the instabilities are qualitatively similar for both the 2D and 3D models, with only minor quantitative differences that relate primarily to the growth speed of the instabilities. The main difference between 2D and 3D models can be found in the spectral energy distributions (SEDs) of the non-thermal particles. The 2D simulations prove to be more efficient, accelerating a larger fraction of the particles and achieving higher velocities. We conclude that, while 2D models are sufficient to investigate the instabilities in the gas, their results have to be treated with some caution when predicting the expected SED of a given shock.

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