scholarly journals Decoding the three-dimensional toric codes and welded codes on cubic lattices

2019 ◽  
Vol 100 (1) ◽  
Author(s):  
Abhishek Kulkarni ◽  
Pradeep Kiran Sarvepalli
Keyword(s):  
Three Dimensional ◽  
Cubic Lattices ◽  
Toric Codes

scholarly journals Phase transition induced by an external field in a three-dimensional isotropic Heisenberg antiferromagnet

2018 ◽  
Vol 32 (32) ◽  
pp. 1850390
Author(s):  
Minos A. Neto ◽  
J. Roberto Viana ◽  
Octavio D. R. Salmon ◽  
E. Bublitz Filho ◽  
José Ricardo de Sousa
Keyword(s):  
Magnetic Field ◽  
Mean Field ◽  
Three Dimensional ◽  
Effective Field ◽  
The Body ◽  
Bravais Lattice ◽  
Body Centered Cubic ◽  
Cubic Lattice ◽  
Cubic Lattices ◽  
Simple Cubic

The critical frontier of the isotropic antiferromagnetic Heisenberg model in a magnetic field along the z-axis has been studied by mean-field and effective-field renormalization group calculations. These methods, abbreviated as MFRG and EFRG, are based on the comparison of two clusters of different sizes, each of them trying to mimic a specific Bravais lattice. The frontier line in the plane of temperature versus magnetic field was obtained for the simple cubic and the body-centered cubic lattices. Spin clusters with sizes N = 1, 2, 4 were used so as to implement MFRG-12, EFRG-12 and EFRG-24 numerical equations. For the simple cubic lattice, the MFRG frontier exhibits a notorious re-entrant behavior. This problem is improved by the EFRG technique. However, both methods agree at lower fields. For the body-centered cubic lattice, the MFRG method did not work. As in the cubic lattice, all the EFRG results agree at lower fields. Nevertheless, the EFRG-12 approach gave no solution for very low temperatures. Comparisons with other methods have been discussed.

scholarly journals Projecting three-dimensional color codes onto three-dimensional toric codes

2018 ◽  
Vol 98 (1) ◽  
Author(s):  
Arun B. Aloshious ◽  
Pradeep Kiran Sarvepalli
Keyword(s):  
Three Dimensional ◽  
Toric Codes

Special directions in momentum space. II. Hexagonal, tetragonal and trigonal symmetries

2012 ◽  
Vol 45 (6) ◽  
pp. 1254-1260 ◽  
Author(s):  
G. Kontrym-Sznajd ◽  
M. Samsel-Czekała
Keyword(s):  
Brillouin Zone ◽  
Momentum Space ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Cubic Lattices ◽  
Whole Space ◽  
Full Symmetry ◽  
Optimal Set ◽  
Three Dimensional Space

This paper is a continuation of a previous one,Special directions in momentum space. I. Cubic symmetries[Kontrym-Sznajd & Samsel-Czekała (2011).J. Appl. Cryst.44, 1246–1254], where new sets of special directions (SDs), having the full symmetry of the Brillouin zone, were proposed for cubic lattices. In the present paper, such directions are derived for structures with unique six-, four- and threefold axes,i.e.hexagonal, tetragonal and trigonal lattices, for both two- and three-dimensional space. The SDs presented here allow for construction, in the whole space, of anisotropic quantities from the knowledge of such quantities along a limited number of SDs. The task at hand is to determine as many anisotropic components as the number of available sampling directions. Also discussed is a way of dealing with data when the number of anisotropic components is restricted by a non-optimal set of SDs.

scholarly journals THE USE OF STRUCTURAL COMPACT MATRIX METHOD FOR CALCULATING THE COM-PACTNESS COEFFICIENT

2021 ◽  
pp. 25-38
Author(s):  
D.V. Fomin ◽  
◽  
E.V. Degtyaryov ◽  
Keyword(s):  
Numerical Methods ◽  
Matrix Method ◽  
Hexagonal Lattice ◽  
Three Dimensional ◽  
Numerical Techniques ◽  
Energy Parameters ◽  
Cubic Lattices ◽  
Matrix Description ◽  
Spatial Configurations

The method of compact matrix description of regular three-dimensional spatial configurations and numerical techniques developed on its basis for calculating some structural and energy parameters of cubic lattices have proved to be more effective in comparison with other numerical methods. The suc-cessful application of the compact matrix method for the description of the simplest hexagonal lattice allows us to develop more efficient numerical methods for calculating the structural and energy pa-rameters of lattices of this type.

Three-dimensional photonic band gaps in modified simple cubic lattices

2002 ◽  
Vol 65 (20) ◽  
Author(s):  
R. Biswas ◽  
M. M. Sigalas ◽  
K.-M. Ho ◽  
S.-Y. Lin
Keyword(s):  
Three Dimensional ◽  
Band Gaps ◽  
Photonic Band Gaps ◽  
Cubic Lattices ◽  
Simple Cubic ◽  
Photonic Band

Resistance calculation of the decorated centered cubic networks: Applications of the Green's function

2014 ◽  
Vol 28 (32) ◽  
pp. 1450252 ◽  
Author(s):  
M. Q. Owaidat ◽  
J. H. Asad ◽  
J. M. Khalifeh
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Function Method ◽  
Three Dimensional ◽  
Numerical Results ◽  
Effective Resistance ◽  
Cubic Lattice ◽  
Cubic Lattices ◽  
Simple Cubic ◽  
Simple Cubic Lattice

The effective resistance between any pair of vertices (sites) on the three-dimensional decorated centered cubic lattices is determined by using lattice Green's function method. Numerical results are presented for infinite decorated centered cubic networks. A mapping between the resistance of the edge-centered cubic lattice and that of the simple cubic lattice is shown.

Generalized difference equation for the three-dimensional Ising ferromagnet

1984 ◽  
Vol 62 (1) ◽  
pp. 35-39 ◽  
Author(s):  
B. Frank ◽  
C. Y. Cheung
Keyword(s):  
Difference Equation ◽  
Correlation Functions ◽  
Three Dimensional ◽  
Ferromagnetic Transition ◽  
Nearest Neighbour ◽  
Ising Ferromagnet ◽  
Cubic Lattices ◽  
Self Consistent ◽  
The Difference ◽  
Single Relation

The difference equation method of Frank, Cheung, and Mouritsen (FCM) is made self-consistent by relaxing an assumption of the theory which pertains to the correlation of a spin with its nearest neighbour. The full set of A = 1 and I − δ equations and U equations is brought into play, with the U2 = T2 = (1/4) (1 − 1/F(1)) double equation replaced by a single relation between U2 and T2. The resulting ferromagnetic transition temperatures for the cubic lattices are consistent with the series results to within about 2%. The correlation functions are much closer to the series results than those of FCM.

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