Coherent potential approximation for the absorption spectra of a two-dimensional Frenkel exciton system with Gaussian diagonal disorder

2014 ◽  
Vol 28 (32) ◽  
pp. 1450251 ◽  
Author(s):  
A. Boukahil ◽  
D. L. Huber
Keyword(s):  
Density Of States ◽  
Reasonable Agreement ◽  
Nearest Neighbor ◽  
Square Lattice ◽  
Two Dimensional ◽  
Frenkel Exciton ◽  
Potential Approximation ◽  
Urbach Tail ◽  
Diagonal Disorder ◽  
Exciton System

We investigate the optical absorption and the density of states of a Frenkel exciton system on a square lattice with nearest-neighbor interactions and a Gaussian distribution of transition frequencies (i.e. Gaussian diagonal disorder). Results are presented for the absorption and the density of states of direct and indirect edge systems for a range of variances. There is reasonable agreement with the corresponding finite array calculations of Schreiber and Toyozawa. The existence of an Urbach tail is also investigated.

scholarly journals Absorption Spectrum and Density of States of Square, Rectangular, and Triangular Frenkel Exciton Systems with Gaussian Diagonal Disorder

2017 ◽  
Vol 2017 ◽  
pp. 1-5
Author(s):  
Ibrahim Avgin ◽  
David Huber
Keyword(s):  
Density Of States ◽  
Nearest Neighbor ◽  
Elliptic Integral ◽  
Coherent Potential Approximation ◽  
Square Lattice ◽  
Integral Approach ◽  
Frenkel Exciton ◽  
Potential Approximation ◽  
Effects Of Disorder ◽  
Diagonal Disorder

Using the coherent potential approximation, we investigate the effects of disorder on the optical absorption and the density of states of Frenkel exciton systems on square, rectangular, and triangular lattices with nearest-neighbor interactions and a Gaussian distribution of transition energies. The analysis is based on an elliptic integral approach that gives results over the entire spectrum. The results for the square lattice are in good agreement with the finite-array calculations of Schreiber and Toyozawa. Our findings suggest that the coherent potential approximation can be useful in interpreting the optical properties of two-dimensional systems with dominant nearest-neighbor interactions and Gaussian diagonal disorder provided the optically active states are Frenkel excitons.

THE CRITICAL BEHAVIOR OF THE 2D SPIN-1 ISING MODEL WITH THE BILINEAR AND POSITIVE BIQUADRATIC NEAREST NEIGHBOR INTERACTIONS ON A CELLULAR AUTOMATON

2004 ◽  
Vol 15 (10) ◽  
pp. 1425-1438 ◽  
Author(s):  
A. SOLAK ◽  
B. KUTLU
Keyword(s):  
Cellular Automaton ◽  
Phase Boundary ◽  
Critical Behavior ◽  
Nearest Neighbor ◽  
Finite Size ◽  
Square Lattice ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Creutz Cellular Automaton ◽  
Beg Model

The two-dimensional BEG model with nearest neighbor bilinear and positive biquadratic interaction is simulated on a cellular automaton, which is based on the Creutz cellular automaton for square lattice. Phase diagrams characterizing phase transitions of the model are presented for comparison with those obtained from other calculations. We confirm the existence of the tricritical points over the phase boundary for D/K>0. The values of static critical exponents (α, β, γ and ν) are estimated within the framework of the finite size scaling theory along D/K=-1 and 1 lines. The results are compatible with the universal Ising critical behavior except the points over phase boundary.

scholarly journals General bounded corner states in two-dimensional off-diagonal Aubry-Andre-Harper model with flat bands

2021 ◽  
Author(s):  
Chao Chen ◽  
Lu Qi ◽  
Yan Xing ◽  
Wen-Xue Cui ◽  
Shou Zhang ◽  
...  
Keyword(s):  
Energy Spectrum ◽  
Lattice Model ◽  
Nearest Neighbor ◽  
Energy Gap ◽  
Real Space ◽  
Lattice System ◽  
Square Lattice ◽  
Two Dimensional ◽  
Zero Energy ◽  
Flat Bands

Abstract We investigate the general bounded corner states in a two-dimensional off-diagonal Aubry-Andre-Harper square lattice model supporting flat bands. We show that for certain values of the nearest-neighbor hopping amplitudes, triply degenerate zero-energy flat bands emerge in this lattice system. Moreover, the two-dimensional off-diagonal Aubry-Andre-Harper model splits into isolated fragments and hosts some general bounded corner states, and the absence of the energy gap results in that these general bounded corner states are susceptible to disorder. By adding the intracellular next-nearest-neighbor hoppings, two flat bands with opposite energies split off from the original triply zero-energy flat bands and some robust general bounded corner states appear in real-space energy spectrum. Our work shows a way to obtain robust general bounded corner states in the two-dimensional off-diagonal Aubry-Andre-Harper model by the intracellular next-nearest-neighbor hoppings.

Ising Antiferromagnet with Nearest-Neighbor and Next-Nearest-Neighbor Interactions on a Square Lattice

2014 ◽  
Vol 215 ◽  
pp. 17-21
Author(s):  
Akai K. Murtazaev ◽  
Magomedsheikh K. Ramazanov ◽  
Magomedzagir K. Badiev
Keyword(s):  
Nearest Neighbor ◽  
Finite Size ◽  
Nearest Neighbors ◽  
Correlation Radius ◽  
Square Lattice ◽  
Two Dimensional ◽  
Critical Properties ◽  
Finite Size Scaling ◽  
Ising Antiferromagnet ◽  
Antiferromagnetic Ising Model

The critical properties of two-dimensional antiferromagnetic Ising model in square lattice are investigated using the replica Monte-Carlo method with account of interactions of second nearest neighbors. The diagram of critical temperature dependence on an interaction value of second nearest neighbors is plotted. Static critical exponents of the heat capacity α, susceptibility γ, magnetization β, and correlation radius ν are calculated for this model using the finite-size scaling theory.

scholarly journals Zero-energy peak of the density of states and localization properties of a one-dimensional Frenkel exciton: Off-diagonal disorder

1998 ◽  
Vol 58 (9) ◽  
pp. 5367-5373 ◽  
Author(s):  
G. G. Kozlov ◽  
V. A. Malyshev ◽  
F. Domínguez-Adame ◽  
A. Rodríguez
Keyword(s):  
Density Of States ◽  
Frenkel Exciton ◽  
Zero Energy ◽  
One Dimensional ◽  
Energy Peak ◽  
Diagonal Disorder

Two-Dimensional Ising Model in an Annealed Random Field

1998 ◽  
Vol 12 (06n07) ◽  
pp. 231-237 ◽  
Author(s):  
C. E. Cordeiro ◽  
L. L. Gonçalves
Keyword(s):  
Ising Model ◽  
Random Field ◽  
Nearest Neighbor ◽  
Chemical Potential ◽  
Square Lattice ◽  
Arbitrary Distribution ◽  
Exchange Constant ◽  
Uniform Field ◽  
Two Dimensional ◽  
Coupled Equations

The critical behavior of the two-dimensional Ising model (square lattice, exchange constant J) in an uniform field, and in an annealed random field is considered. The random field is generated by decorating the horizontal and vertical bonds of the lattice, and it satisfies an arbitrary distribution which is imposed by introducing a pseudo-chemical potential. By decimating the decorating variables the model can be mapped onto a homogeneous Ising model with effective exchange constant J′ and effective external field h′, dependent on the temperature. These parameters, which satisfy a set of coupled equations, depend on the spin average and nearest-neighbor two-spin correlation, and are obtained numerically. For the symmetric field distribution [Formula: see text] the mapping of the critical frontier on the (K′=βJ′,H′=βh′) plane onto the (K=β J,H=βh) plane is determined and, as in the model introduced by Essam and Place, there is a region on the (K, H) plane which cannot be reached from any real values of (K′, H′). The critical exponents are determined numerically, and it is shown that they do not satisfy renormalization relations obtained for their model.

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