Transfer matrices for first-, second- and third-neighbor interactions on two-dimensional, hexagonal-cell lattices

1991 ◽  
Vol 175 (2) ◽  
pp. 305-326 ◽  
Author(s):  
R.B. McQuistan ◽  
J.L. Hock
Keyword(s):  
Two Dimensional ◽  
Transfer Matrices ◽  
Hexagonal Cell

scholarly journals GENERALIZED YANG-BAXTER EQUATION

1993 ◽  
Vol 08 (24) ◽  
pp. 2299-2309 ◽  
Author(s):  
R. M. KASHAEV ◽  
YU. G. STROGANOV
Keyword(s):  
Single Layer ◽  
Lattice Models ◽  
Baxter Equation ◽  
Explicit Solutions ◽  
Generalized Equations ◽  
Two Dimensional ◽  
Layer Transfer ◽  
Transfer Matrices ◽  
Dimensional Lattice ◽  
Potts Models

A generalization of the Yang-Baxter equation is proposed. It enables us to construct integrable two-dimensional lattice models with commuting two-layer transfer matrices, while single-layer ones are not necessarily commutative. Explicit solutions to the generalized equations are found. They are related with Boltzmann weights of the sl (3) chiral Potts models.

scholarly journals On the Combinatorics of Row and Corner Transfer Matrices of the $A^{(1)}_{n-1}$ Restricted Face Models

1997 ◽  
Vol 12 (20) ◽  
pp. 3551-3586 ◽  
Author(s):  
Srinandan Dasmahapatra
Keyword(s):  
Spectral Data ◽  
Polynomial Identity ◽  
Spin Chain ◽  
Two Dimensional ◽  
Transfer Matrices ◽  
Dimensional Model ◽  
Corner Transfer Matrices ◽  
Weight Lattice ◽  
Index Sets ◽  
Two Dimensional Model

We establish a weight-preserving bijection between the index sets of the spectral data of row-to-row and corner transfer matrices for [Formula: see text] restricted interaction round a face (IRF) models. The evaluation of momenta by adding Takahashi integers in the spin chain language is shown to directly correspond to the computation of the energy of a path on the weight lattice in the two-dimensional model. As a consequence we derive fermionic forms of polynomial analogs of branching functions for the cosets [Formula: see text], and establish a bosonic–fermionic polynomial identity.

ELECTRONIC STRUCTURE OF GRAPHENE AND GERMANENE BASED ON DOUBLE HEXAGONAL STRUCTURE

2013 ◽  
Vol 27 (29) ◽  
pp. 1350212 ◽  
Author(s):  
S. NAJI ◽  
A. BELHAJ ◽  
H. LABRIM ◽  
A. BENYOUSSEF ◽  
A. EL KENZ
Keyword(s):  
Electronic Structure ◽  
Ab Initio Calculations ◽  
Ab Initio ◽  
Hexagonal Structure ◽  
Lattice Parameters ◽  
Two Dimensional ◽  
Atomic Configuration ◽  
Hexagonal Cell ◽  
Exceptional Lie Algebra ◽  
Principal Unit

In this paper, we study the electronic structure of monolayer materials based on a double hexagonal geometry with (1×1) and [Formula: see text] superstructures. Inspired from the two-dimensional root system of an exceptional Lie algebra called G2, this hexagonal atomic configuration involves two hexagons of unequal side length at angle 30°. The principal unit hexagonal cell contains twelve atoms instead of the usual configuration involving only six ones relying only on the (1×1) superstructure. Using ab initio calculations based on FPLO9.00-34 code, we investigate numerically the graphene and the germanene with the double hexagonal geometry. In particular, we find that the usual electronic properties and the lattice parameters of such materials are modified. More precisely, the lattice parameters are increased. It has been shown that, in the single hexagonal geometry, the grapheme and the germanene behave as a gapless semiconductor and a semi-metallic, respectively. In double hexagonal geometry however, both materials becomes metallic.

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