SU(2) deconfinement temperature on a body-centered hypercubic lattice

1986 ◽  
Vol 33 (10) ◽  
pp. 3022-3030 ◽  
Author(s):  
W. Celmaster ◽  
Eve Kovács ◽  
F. Green ◽  
R. Gupta
Keyword(s):  
Hypercubic Lattice

SU(2) quark potential on a body-centered-hypercubic lattice

1986 ◽  
Vol 33 (12) ◽  
pp. 3718-3732 ◽  
Author(s):  
William Celmaster ◽  
K. J. M. Moriarty
Keyword(s):  
Hypercubic Lattice ◽  
Quark Potential

Extended high temperature low field expansions for the Ising model

1979 ◽  
Vol 57 (8) ◽  
pp. 1239-1245 ◽  
Author(s):  
S. McKenzie
Keyword(s):  
Free Energy ◽  
High Temperature ◽  
Ising Model ◽  
Three Dimensional ◽  
Low Field ◽  
Hypercubic Lattice

High temperature low field expansions are derived from the free energy of the Ising model for several two- and three-dimensional lattices. These represent a considerable advance on earlier work. Expansions for the four-dimensional hypercubic lattice are also presented.

scholarly journals Average unit cell for the Generalized Penrose Tiling

2014 ◽  
Vol 70 (a1) ◽  
pp. C88-C88
Author(s):  
Maciej Chodyn ◽  
Pawel Kuczera ◽  
Janusz Wolny
Keyword(s):  
Single Point ◽  
Analytical Formula ◽  
Unit Cell ◽  
The Body ◽  
Penrose Tiling ◽  
Shift Parameter ◽  
Decagonal Quasicrystal ◽  
Promising Alternative ◽  
Hypercubic Lattice ◽  
Average Unit

The Generalized Penrose Tiling (GPT) can be considered a promising alternative for Penrose Tiling (PT) as a model for decagonal quasicrystal refinement procedure, particularly in the statistical approach (also called the Average Unit Cell (AUC) approach) [1]. The statistical method using PT has been successfully applied to the structure optimization of various decagonal phases [2]. The application of the AUC concept to the GPT will be presented. In the higher dimensional (nD) approach, PT is obtained by projecting a 5D hypercubic lattice through a window consisting of four pentagons, called the atomic surfaces (ASs), in the perpendicular space. The vertices of these pentagons together with two additional points form a rhombicosahedron. The GPT is created by projecting the 5D hypercubic lattice through a window consisting of five polygons, generated by shifting the ASs along the body diagonal of the rhombicosahedron. Three of the previously pentagonal ASs will become decagon, one will remain pentagonal and one more pentagon will be created (for PT it is a single point). The structure of GPT will depend on the shift parameter, its building units are still thick and thin rhombuses, but the matching rules and the tiling changes. In the AUC concept the probability distribution for rhombuses of PT can be obtained as an oblique projection of the ASs on the physical space. This holds true also for the GPT. The derivation of the AUC distribution for a given type of rhomb in a given orientation of an arbitrarily chosen GPT will be presented. In the PT, these distributions are triangular, whereas in the case of the GPT they are triangular (originating from the pentagonal AS) or hexagonal (originating from the decagonal AS). The AUC of GPT for shift parameters 0.2 and 0.5 has been calculated. The derivation of the analytical formula for structure factor using AUC formalism, for the decorated GPT is made similarly to the calculation for the PT [3].

THE ROOT LATTICE D4 AND PLANAR QUASILATTICES WITH OCTAGONAL AND DODECAGONAL SYMMETRY

1991 ◽  
Vol 05 (11) ◽  
pp. 1927-1953 ◽  
Author(s):  
M. BAAKE ◽  
D. JOSEPH ◽  
M. SCHLOTTMANN
Keyword(s):  
Root Lattice ◽  
Dihedral Groups ◽  
Hypercubic Lattice ◽  
Face Centered ◽  
Two Phases ◽  
Minimal Embedding

Quasiperiodic patterns with eight- and twelvefold symmetry are presented which share the root lattice D4, i.e., the 4-D face-centered hypercubic lattice, for their minimal embedding in four-space. We derive the patterns by means of the dualization method and investigate key properties like vertex configurations, local deflation/inflation symmetries and kinematic diffraction. The generalized point symmetries (and thus the Laue group) of these patterns are the dihedral groups d8 and d12, respectively, which share a common subgroup, d4. We introduce a contiunous one-parameter rotation between the two phases which leaves this subgroup invariant. This should prove useful for modelling alloys like V 15 Ni 10 Si where quasicrystalline phases with eight- and twelvefold symmetry coexist.

Surfaces in the hypercubic lattice

1992 ◽  
Vol 25 (12) ◽  
pp. 3529-3547 ◽  
Author(s):  
E J Janse van Rensburg
Keyword(s):  
Hypercubic Lattice
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