IS THERE A DELOCALISATION TRANSITION IN A TWO-DIMENSIONAL MODEL FOR QUANTUM PERCOLATION?

1992 ◽  
Vol 06 (13) ◽  
pp. 817-821 ◽  
Author(s):  
INDRA DASGUPTA ◽  
TANUSRI SAHA ◽  
ABHIJIT MOOKERJEE ◽  
B. K. CHAKRABARTI
Keyword(s):  
Finite Size ◽  
Two Dimensions ◽  
Percolation Model ◽  
Square Lattice ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Dimensional Model ◽  
Recursion Method ◽  
Quantum Percolation ◽  
Two Dimensional Model

We estimate the transmittance of the quantum percolation model of Eggarter and Kirkpatrick (1972) on the square lattice of various sizes using the vector recursion method. We note from finite size scaling that there is no delocalisation transition for any degree of disorder in two dimensions.

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.

THE SIMULATION OF 2D SPIN-1 ISING MODEL WITH POSITIVE BIQUADRATIC INTERACTION ON A CELLULAR AUTOMATON

2003 ◽  
Vol 14 (10) ◽  
pp. 1305-1320 ◽  
Author(s):  
BÜLENT KUTLU
Keyword(s):  
Phase Transition ◽  
Ising Model ◽  
Cellular Automaton ◽  
Intermediate Phase ◽  
Finite Size ◽  
Square Lattice ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Creutz Cellular Automaton ◽  
Antiferromagnetic Spin

The two-dimensional antiferromagnetic spin-1 Ising model with positive biquadratic interaction is simulated on a cellular automaton which based on the Creutz cellular automaton for square lattice. Phase diagrams characterizing phase transition of the model are presented for a comparison with those obtained from other calculations. We confirm the existence of the intermediate phase observed in previous works for some values of J/K and D/K. The values of the static critical exponents (β, γ and ν) are estimated within the framework of the finite-size scaling theory for D/K<2J/K. Although the results are compatible with the universal Ising critical behavior in the region of D/K<2J/K-4, the model does not exhibit any universal behavior in the interval 2J/K-4<D/K<2J/K.

ON THE SELF-CONSISTENT STATISTICAL THEORY OF STRUCTURAL, DYNAMICAL, AND THERMODYNAMIC SURFACE PROPERTIES OF ANHARMONIC CRYSTALS II: The Properties of Arbitrary Oriented Surfaces of the Two-Dimensional Model with Square Lattice

1990 ◽  
Vol 04 (03) ◽  
pp. 479-499
Author(s):  
V. I. ZUBOV ◽  
F. BANYERETSE
Keyword(s):  
Surface Properties ◽  
Lattice Relaxation ◽  
Field Method ◽  
Square Lattice ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Anharmonic Crystal ◽  
Thermodynamic Surface ◽  
Self Consistent ◽  
Two Dimensional Model

The correlative unsymmetrized self-consistent field method is used to study surface properties of the two-dimensional model of an anharmonic crystal with square lattice having various Miller indices. The lattice relaxation, the amplitudes of atomic vibrations and the thermodynamic surface functions are calculated. The typical nonsingular and vicinal surfaces are considered. The dependence of thermodynamic surface functions on the surface orientation is obtained.

The Waltzian ordering principle and international change: A two-dimensional model

2017 ◽  
Vol 24 (1) ◽  
pp. 130-152 ◽  
Author(s):  
Ryan D. Griffiths
Keyword(s):  
Structural Realism ◽  
Functional Differentiation ◽  
International Order ◽  
Two Dimensions ◽  
The Other ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Ideal Types ◽  
Classical Path ◽  
Two Dimensional Model

In his work on structural realism, Kenneth Waltz developed a theory of international order that is admired for its parsimony but criticized for its simplicity. Using his ordering principle as a foundation, I critique and extend his theory by constructing a model of international order with two dimensions: one of political centralization and the other of segmentary/functional differentiation. The resulting map locates different configurations of order and highlights four ideal-types: mechanical anarchy, organic hierarchy, mechanical hierarchy and organic anarchy. I then use the two-dimensional map and related ideal-types to outline two different processes of international change — a classical path and a modern path — that were invisible in the Waltzian model. This article is thus a contribution to the developing literature on conceptualizing different forms of international order and the dynamics of international change.

Modeling Flash Diffusivity Experiments in Two Dimensions for Thick Samples

2008 ◽  
Author(s):  
Robert L. McMasters
Keyword(s):  
Experimental Data ◽  
Laser Flash ◽  
Two Dimensions ◽  
Flash Method ◽  
Two Dimensional ◽  
Dimensional Model ◽  
One Dimensional ◽  
Two Dimensional Model ◽  
Dimensional Analysis Method ◽  
Flash Diffusivity

The laser flash method for measuring thermal diffusivity is well established and has been in use for many years. Early analysis methods employed a simple model, in which one dimensional transient conduction was assumed, with insulated surfaces during the time subsequent to the flash. More recently, models of grater sophistication have been applied to flash diffusivity experiments. These models have been matched to experimental data using nonlinear regression and assume one-dimensional conduction. The advanced models have achieved highly accurate agreement with experimental data taken from thin samples, on the order of one millimeter in thickness. As samples become thicker, models which neglect edge losses can lose some conformity to the experimental data. The present research involves the application of a two dimensional model which allows for penetration of the laser flash into the sample. The accommodation of the flash penetration is important for porous materials, where the coarseness of the porosity is more than one percent of the sample thickness. Variability of the area of incidence of the flash is also investigated to determine the effect on the model and the results. Statistical methods are used in order to make a determination as to the validity of the two dimensional model, as compared with the one dimensional analysis method.

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 Anisotropic scaling of the two-dimensional Ising model I: the torus

2019 ◽  
Vol 7 (3) ◽  
Author(s):  
Hendrik Hobrecht ◽  
Fred Hucht
Keyword(s):  
Free Energy ◽  
Ising Model ◽  
Boundary Conditions ◽  
Scaling Limit ◽  
Finite Size ◽  
Square Lattice ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Anisotropic Scaling

We present detailed calculations for the partition function and the free energy of the finite two-dimensional square lattice Ising model with periodic and antiperiodic boundary conditions, variable aspect ratio, and anisotropic couplings, as well as for the corresponding universal free energy finite-size scaling functions. Therefore, we review the dimer mapping, as well as the interplay between its topology and the different types of boundary conditions. As a central result, we show how both the finite system as well as the scaling form decay into contributions for the bulk, a characteristic finite-size part, and – if present – the surface tension, which emerges due to at least one antiperiodic boundary in the system. For the scaling limit we extend the proper finite-size scaling theory to the anisotropic case and show how this anisotropy can be absorbed into suitable scaling variables.

THE SIMULATION OF THE 2D FERROMAGNETIC BLUME–CAPEL MODEL ON A CELLULAR AUTOMATON

2001 ◽  
Vol 12 (09) ◽  
pp. 1401-1413 ◽  
Author(s):  
B. KUTLU
Keyword(s):  
Critical Temperature ◽  
Cellular Automaton ◽  
Critical Behavior ◽  
Critical Exponents ◽  
Finite Size ◽  
Scaling Theory ◽  
Square Lattice ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Creutz Cellular Automaton

The two-dimensional ferromagnetic Blume–Capel model is simulated on a cellular automaton, which based on the Creutz cellular automaton for square lattice. The values of the critical temperature and the static critical exponents are estimated within the framework of the finite-size scaling theory for 0 ≤ D/J ≤ 1.5. The results are compatible with the universal Ising critical behavior.

scholarly journals A data-driven study of Chinese participants’ social judgments of Chinese faces

2018 ◽  
Author(s):  
Hongyi Wang ◽  
Chengyang Han ◽  
Amanda Hahn ◽  
Vanessa Fasolt ◽  
Danielle Morrison ◽  
...  
Keyword(s):  
Cultural Differences ◽  
Two Dimensions ◽  
Data Driven ◽  
Two Dimensional ◽  
Social Judgments ◽  
Dimensional Model ◽  
Present Evidence ◽  
Two Dimensional Model ◽  
Data Driven Approach

Social judgments of faces made by Western participants are thought to be underpinned by two dimensions: valence and dominance. Because some research suggests that Western and Eastern participants process faces differently, the two-dimensional model of face evaluation may not necessarily apply to judgments of faces by Eastern participants. Here we used a data-driven approach to investigate the components underlying social judgments of Chinese faces by Chinese participants. Analyses showed that social judgments of Chinese faces by Chinese participants are partly underpinned by a general approachability dimension similar to the valence dimension previously found to underpin Western participants’ evaluations of White faces. However, we found that a general capability dimension, rather than a dominance dimension, contributed to Chinese participants’ evaluations of Chinese faces. Thus, our findings present evidence for both cultural similarities and cultural differences in social evaluations of faces. Importantly, the dimension that explained most of the variance in Chinese participants’ social judgments of faces was strikingly similar to the valence dimension previously reported for Western participants.

scholarly journals Rayleigh-Bénard convection of a model emulsion: anomalous heat-flux fluctuations and finite-size droplets effects

Soft Matter ◽  
2021 ◽  
Author(s):  
Francesca Pelusi ◽  
Mauro Sbragaglia ◽  
Roberto Benzi ◽  
Andrea Scagliarini ◽  
Massimo Bernaschi ◽  
...  
Keyword(s):  
Heat Flux ◽  
Numerical Simulations ◽  
Finite Size ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Two Dimensional Model ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Model Emulsion ◽  
Anomalous Heat

We present mesoscale numerical simulations of Rayleigh-Bénard (RB) convection in a two-dimensional model emulsion. The systems under study are constituted of finite-size droplets, whose concentration Ψ0 is systematically varied from...

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