scholarly journals Exact and Approximate Theoretical Techniques for Quantum Magnetism in Low Dimensions

2003 ◽  
pp. 119-171
Author(s):  
Swapan K. Pati ◽  
S. Ramasesha ◽  
Diptiman Sen
Keyword(s):  
Quantum Magnetism ◽  
Low Dimensions

scholarly journals Exact and Approximate Theoretical Techniques for Quantum Magnetism in Low Dimensions

ChemInform ◽  
2003 ◽  
Vol 34 (38) ◽  
Author(s):  
Swapan K. Pati ◽  
S. Ramasesha ◽  
Diptiman Sen
Keyword(s):  
Quantum Magnetism ◽  
Low Dimensions

scholarly journals Van Hove singularity in the magnon spectrum of the antiferromagnetic quantum honeycomb lattice

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
G. Sala ◽  
M. B. Stone ◽  
Binod K. Rai ◽  
A. F. May ◽  
Pontus Laurell ◽  
...  
Keyword(s):  
Disordered Systems ◽  
Inelastic Neutron Scattering ◽  
Magnetic Moments ◽  
Wave Theory ◽  
Inelastic Neutron ◽  
Quantum Spin ◽  
Honeycomb Lattice ◽  
Quantum Magnetism ◽  
Van Hove Singularity ◽  
Sharp Feature

AbstractIn quantum magnets, magnetic moments fluctuate heavily and are strongly entangled with each other, a fundamental distinction from classical magnetism. Here, with inelastic neutron scattering measurements, we probe the spin correlations of the honeycomb lattice quantum magnet YbCl3. A linear spin wave theory with a single Heisenberg interaction on the honeycomb lattice, including both transverse and longitudinal channels of the neutron response, reproduces all of the key features in the spectrum. In particular, we identify a Van Hove singularity, a clearly observable sharp feature within a continuum response. The demonstration of such a Van Hove singularity in a two-magnon continuum is important as a confirmation of broadly held notions of continua in quantum magnetism and additionally because analogous features in two-spinon continua could be used to distinguish quantum spin liquids from merely disordered systems. These results establish YbCl3 as a benchmark material for quantum magnetism on the honeycomb lattice.

scholarly journals FRACTAL DIMENSION OF SPIN-GLASSES INTERFACES IN DIMENSION d = 2 AND d = 3 VIA STRONG DISORDER RENORMALIZATION AT ZERO TEMPERATURE

Fractals ◽  
2015 ◽  
Vol 23 (04) ◽  
pp. 1550042 ◽  
Author(s):  
CÉCILE MONTHUS
Keyword(s):  
Fractal Dimension ◽  
Boundary Conditions ◽  
Spin Glasses ◽  
Periodic Boundary ◽  
Domain Walls ◽  
Numerical Study ◽  
Periodic Boundary Conditions ◽  
Zero Temperature ◽  
Low Dimensions ◽  
Strong Disorder

For Gaussian Spin-Glasses in low dimensions, we introduce a simple Strong Disorder renormalization at zero temperature in order to construct ground states for Periodic and Anti-Periodic boundary conditions. The numerical study in dimensions [Formula: see text] (up to sizes [Formula: see text]) and [Formula: see text] (up to sizes [Formula: see text]) yields that Domain Walls are fractal of dimensions [Formula: see text] and [Formula: see text], respectively.

Classification of Filiform Leibniz Algebras in Low Dimensions

2019 ◽  
pp. 223-249
Author(s):  
Shavkat Ayupov ◽  
Bakhrom Omirov ◽  
Isamiddin Rakhimov
Keyword(s):  
Low Dimensions ◽  
Leibniz Algebras

scholarly journals Engineering block copolymer materials for patterning ultra-low dimensions

2020 ◽  
Vol 5 (10) ◽  
pp. 1642-1657
Author(s):  
Cian Cummins ◽  
Guillaume Pino ◽  
Daniele Mantione ◽  
Guillaume Fleury
Keyword(s):  
Thin Film ◽  
Block Copolymer ◽  
Block Copolymers ◽  
Low Dimensions ◽  
Processing Strategies ◽  
Synthetic Routes ◽  
Film Processing ◽  
Thin Film Processing

Recently engineered high χ-low N block copolymers for nanolithography are evaluated. Synthetic routes together with thin film processing strategies are highlighted that could enable the relentless scaling for logic technologies at sub-10 nanometres.

scholarly journals Estimating perimeter using graph cuts

2017 ◽  
Vol 49 (4) ◽  
pp. 1067-1090 ◽  
Author(s):  
Nicolás García Trillos ◽  
Dejan Slepčev ◽  
James von Brecht
Keyword(s):  
Confidence Intervals ◽  
Error Estimates ◽  
Approximation Error ◽  
Higher Dimensions ◽  
Geometric Graph ◽  
Graph Cut ◽  
Average Degree ◽  
Random Geometric Graph ◽  
Low Dimensions ◽  
Variance Estimates

Abstract We investigate the estimation of the perimeter of a set by a graph cut of a random geometric graph. For Ω ⊆ D = (0, 1)d with d ≥ 2, we are given n random independent and identically distributed points on D whose membership in Ω is known. We consider the sample as a random geometric graph with connection distance ε > 0. We estimate the perimeter of Ω (relative to D) by the, appropriately rescaled, graph cut between the vertices in Ω and the vertices in D ∖ Ω. We obtain bias and variance estimates on the error, which are optimal in scaling with respect to n and ε. We consider two scaling regimes: the dense (when the average degree of the vertices goes to ∞) and the sparse one (when the degree goes to 0). In the dense regime, there is a crossover in the nature of the approximation at dimension d = 5: we show that in low dimensions d = 2, 3, 4 one can obtain confidence intervals for the approximation error, while in higher dimensions one can obtain only error estimates for testing the hypothesis that the perimeter is less than a given number.

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