COUPLING CONSTANT AND MAGNON VELOCITY FOR A TWO-DIMENSIONAL QUANTUM HEISENBERG ANTIFERROMAGNET: THE CONTINUUM LIMIT

1996 ◽  
Vol 10 (28) ◽  
pp. 1389-1395 ◽  
Author(s):  
SIMON VILLAIN-GUILLOT ◽  
ROSSEN DANDOLOFF
Keyword(s):  
Degrees Of Freedom ◽  
Continuum Limit ◽  
Two Dimensions ◽  
Infinite Plane ◽  
Heisenberg Antiferromagnet ◽  
Coupling Constant ◽  
Covariant Derivatives ◽  
Heisenberg Hamiltonian ◽  
Derivatives Of ◽  
The Continuum

We study Heisenberg spins on an infinite plane. Following an approach developed by Affleck, we find that the Heisenberg Hamiltonian is equivalent in the continuum limit to the nonlinear σ model. And we show that the auxiliary fields, which appear because of the conservation of the number of degrees of freedom, are related to the covariant derivatives of the order parameter. These auxiliary fields have to be taken into account in order to recover the expected values for the coupling constant and magnon velocity in two-dimensions.

scholarly journals Charm sea effects on charmonium decay constants and heavy meson masses

2021 ◽  
Vol 81 (8) ◽  
Author(s):  
Salvatore Calì ◽  
Kevin Eckert ◽  
Jochen Heitger ◽  
Francesco Knechtli ◽  
Tomasz Korzec
Keyword(s):  
Lattice Qcd ◽  
Continuum Limit ◽  
Charm Quark ◽  
Heavy Meson ◽  
Charm Quarks ◽  
Decay Constants ◽  
Derivatives Of ◽  
Charm Mass ◽  
The Continuum

AbstractWe estimate the effects on the decay constants of charmonium and on heavy meson masses due to the charm quark in the sea. Our goal is to understand whether for these quantities $${N_\mathrm{f}}=2+1$$ N f = 2 + 1 lattice QCD simulations provide results that can be compared with experiments or whether $${N_\mathrm{f}}=2+1+1$$ N f = 2 + 1 + 1 QCD including the charm quark in the sea needs to be simulated. We consider two theories, $${N_\mathrm{f}}=0$$ N f = 0 QCD and QCD with $${N_\mathrm{f}}=2$$ N f = 2 charm quarks in the sea. The charm sea effects (due to two charm quarks) are estimated comparing the results obtained in these two theories, after matching them and taking the continuum limit. The absence of light quarks allows us to simulate the $${N_\mathrm{f}}=2$$ N f = 2 theory at lattice spacings down to 0.023 fm that are crucial for reliable continuum extrapolations. We find that sea charm quark effects are below 1% for the decay constants of charmonium. Our results show that decoupling of charm works well up to energies of about 500 MeV. We also compute the derivatives of the decay constants and meson masses with respect to the charm mass. For these quantities we again do not see a significant dynamical charm quark effect, albeit with a lower precision. For mesons made of a charm quark and a heavy antiquark, whose mass is twice that of the charm quark, sea effects are only about 1‰ in the ratio of vector to pseudoscalar masses.

NONLINEAR FIELD ANALYSIS OF THE HUBBARD MODEL IN ONE AND TWO DIMENSIONS IN THE CONTINUUM LIMIT

2000 ◽  
Vol 14 (18) ◽  
pp. 1859-1890
Author(s):  
J. M. DIXON ◽  
J. A. TUSZYŃSKI ◽  
M. L. A. NIP ◽  
D. SEPT ◽  
K. J. E. VOS
Keyword(s):  
Continuum Limit ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Two Dimensions ◽  
Field Analysis ◽  
Field Equations ◽  
Phase Dynamics ◽  
Hartree Fock ◽  
Spin Fields ◽  
The Continuum

We investigate the Hubbard Hamiltonian's properties in the continuum limit by implementing the procedures of the Method of Coherent Structures (MCS). We obtain field equations of motion and analyse the phase dynamics of the resultant classical spin fields. We have performed analytical and numerical calculations to find appropriate physically acceptable solutions to the equations of motion in one-dimensional space. In two-dimensional space, among other types, we have found several different spin phases of vortex type, spiral patterns and parabolic spin arrangements. Our results are consistent with earlier Hartree–Fock finite-grid numerical simulations.

CHO DECOMPOSITION OF ONE-HALF INTEGER MONOPOLES SOLUTIONS

2013 ◽  
Vol 28 (30) ◽  
pp. 1350144 ◽  
Author(s):  
ROSY TEH ◽  
BAN-LOONG NG ◽  
KHAI-MING WONG
Keyword(s):  
Total Energy ◽  
Higgs Field ◽  
Finite Energy ◽  
Coupling Constant ◽  
Yang Mills ◽  
Half Integer ◽  
Covariant Derivatives ◽  
Monopole Solution ◽  
The One ◽  
Derivatives Of

We performed the Cho decomposition of the SU(2) Yang–Mills–Higgs gauge potentials of the finite energy (1) one-half monopole solution and (2) the one and a half monopoles solution into Abelian and non-Abelian components. We found that the semi-infinite string singularity in the gauge potentials is a contribution from the Higgs field of the one-half monopole in both of the solutions. The non-Abelian components of the gauge potentials are able to remove the point singularity of the Abelian components of the 't Hooft–Polyakov monopole but not the string singularity of the one-half monopole which is topological in nature. Hence the total energy of a one monopole is infinite in the Maxwell electromagnetic theory but the total energy of a one-half monopole is finite. By analyzing the magnetic fields and the gauge covariant derivatives of the Higgs field, we are able to conclude that both the one-half integer monopoles solutions are indeed non-BPS even in the limit of vanishing Higgs self-coupling constant.

scholarly journals THE ANTIFERROMAGNETIC POTTS MODEL

2011 ◽  
Vol 25 (05) ◽  
pp. 291-313 ◽  
Author(s):  
YACINE IKHLEF
Keyword(s):  
Bethe Ansatz ◽  
Potts Model ◽  
Degrees Of Freedom ◽  
Continuum Limit ◽  
Exact Results ◽  
Antiferromagnetic Potts Model ◽  
Ansatz Approach ◽  
The Continuum

We review the exact results on the various critical regimes of the antiferromagnetic Q-state Potts model. We focus on the Bethe Ansatz approach for generic Q, and describe in each case the effective degrees of freedom appearing in the continuum limit.

scholarly journals Analysis of Artifacts in Shell-Based Image Inpainting: Why They Occur and How to Eliminate Them

2020 ◽  
Vol 20 (6) ◽  
pp. 1549-1651
Author(s):  
L. Robert Hocking ◽  
Thomas Holding ◽  
Carola-Bibiane Schönlieb
Keyword(s):  
Theoretical Model ◽  
Degrees Of Freedom ◽  
Continuum Limit ◽  
Direct Method ◽  
Image Inpainting ◽  
Weighted Average ◽  
Numerical Linear Algebra ◽  
Image Pixels ◽  
Stopped Random Walks ◽  
The Continuum

AbstractIn this paper we study a class of fast geometric image inpainting methods based on the idea of filling the inpainting domain in successive shells from its boundary inwards. Image pixels are filled by assigning them a color equal to a weighted average of their already filled neighbors. However, there is flexibility in terms of the order in which pixels are filled, the weights used for averaging, and the neighborhood that is averaged over. Varying these degrees of freedom leads to different algorithms, and indeed the literature contains several methods falling into this general class. All of them are very fast, but at the same time all of them leave undesirable artifacts such as “kinking” (bending) or blurring of extrapolated isophotes. Our objective in this paper is to build a theoretical model in order to understand why these artifacts occur and what, if anything, can be done about them. Our model is based on two distinct limits: a continuum limit in which the pixel width $$h \rightarrow 0$$ h → 0 and an asymptotic limit in which $$h > 0$$ h > 0 but $$h \ll 1$$ h ≪ 1 . The former will allow us to explain “kinking” artifacts (and what to do about them) while the latter will allow us to understand blur. Both limits are derived based on a connection between the class of algorithms under consideration and stopped random walks. At the same time, we consider a semi-implicit extension in which pixels in a given shell are solved for simultaneously by solving a linear system. We prove (within the continuum limit) that this extension is able to completely eliminate kinking artifacts, which we also prove must always be present in the direct method. Finally, we show that although our results are derived in the context of inpainting, they are in fact abstract results that apply more generally. As an example, we show how our theory can also be applied to a problem in numerical linear algebra.

Instability and Collapse in Discrete Wave Equations

2005 ◽  
Vol 5 (3) ◽  
pp. 223-241
Author(s):  
A. Carpio ◽  
G. Duro
Keyword(s):  
Continuum Limit ◽  
Wave Equations ◽  
Numerical Solutions ◽  
Blow Up ◽  
Theoretical Predictions ◽  
Initial States ◽  
The Impact ◽  
The Continuum

AbstractUnstable growth phenomena in spatially discrete wave equations are studied. We characterize sets of initial states leading to instability and collapse and obtain analytical predictions for the blow-up time. The theoretical predictions are con- trasted with the numerical solutions computed by a variety of schemes. The behavior of the systems in the continuum limit and the impact of discreteness and friction are discussed.

Holomorphically projective mappings between generalized m-parabolic Kähler manifolds

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4865-4873 ◽  
Author(s):  
Milos Petrovic
Keyword(s):  
Linear Systems ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Covariant Derivatives ◽  
Linearly Independent ◽  
Non Linear ◽  
Non Linear Systems ◽  
Curvature Tensors ◽  
Derivatives Of

Generalized m-parabolic K?hler manifolds are defined and holomorphically projective mappings between such manifolds have been considered. Two non-linear systems of PDE?s in covariant derivatives of the first and second kind for the existence of such mappings are given. Also, relations between five linearly independent curvature tensors of generalized m-parabolic K?hler manifolds with respect to these mappings are examined.

scholarly journals From Center-Vortex Ensembles to the Confining Flux Tube

Universe ◽  
2021 ◽  
Vol 7 (8) ◽  
pp. 253
Author(s):  
David R. Junior ◽  
Luis E. Oxman ◽  
Gustavo M. Simões
Keyword(s):  
Degrees Of Freedom ◽  
String Tension ◽  
Effective Field ◽  
Scaling Properties ◽  
Flux Tubes ◽  
Topological Solitons ◽  
Yang Mills ◽  
Center Vortex ◽  
Asymptotic Scaling ◽  
The Continuum

In this review, we discuss the present status of the description of confining flux tubes in SU(N) pure Yang–Mills theory in terms of ensembles of percolating center vortices. This is based on three main pillars: modeling in the continuum the ensemble components detected in the lattice, the derivation of effective field representations, and contrasting the associated properties with Monte Carlo lattice results. The integration of the present knowledge about these points is essential to get closer to a unified physical picture for confinement. Here, we shall emphasize the last advances, which point to the importance of including the non-oriented center-vortex component and non-Abelian degrees of freedom when modeling the center-vortex ensemble measure. These inputs are responsible for the emergence of topological solitons and the possibility of accommodating the asymptotic scaling properties of the confining string tension.

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