scholarly journals Fractal Configurations of the Two- and Three-Dimensional Ising Models at the Critical Point

1987 ◽  
Vol 77 (6) ◽  
pp. 1391-1401 ◽  
Author(s):  
N. Ito ◽  
M. Suzuki
Keyword(s):  
Critical Point ◽  
Three Dimensional ◽  
Ising Models

scholarly journals Analytical Expressions for Ising Models on High Dimensional Lattices

Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1665
Author(s):  
Boris Kryzhanovsky ◽  
Leonid Litinskii ◽  
Vladislav Egorov
Keyword(s):  
Critical Point ◽  
Three Dimensional ◽  
Ising Models ◽  
High Dimensional ◽  
High Dimensions ◽  
Critical Temperatures ◽  
Dimensional Lattice ◽  
Long Range Interactions ◽  
Analytical Expressions ◽  
Good Agreement

We use an m-vicinity method to examine Ising models on hypercube lattices of high dimensions d ≥ 3. This method is applicable for both short-range and long-range interactions. We introduce a small parameter, which determines whether the method can be used when calculating the free energy. When we account for interaction with the nearest neighbors only, the value of this parameter depends on the dimension of the lattice d. We obtain an expression for the critical temperature in terms of the interaction constants that is in a good agreement with the results of computer simulations. For d = 5,6,7, our theoretical estimates match the numerical results both qualitatively and quantitatively. For d = 3,4, our method is sufficiently accurate for the calculation of the critical temperatures; however, it predicts a finite jump of the heat capacity at the critical point. In the case of the three-dimensional lattice (d = 3), this contradicts the commonly accepted ideas of the type of the singularity at the critical point. For the four-dimensional lattice (d = 4), the character of the singularity is under current discussion. For the dimensions d = 1,2 the m-vicinity method is not applicable.

Nucleation and metastability in three-dimensional Ising models

1984 ◽  
Vol 36 (3-4) ◽  
pp. 447-470 ◽  
Author(s):  
Dieter W. Heermann ◽  
Antonio Coniglio ◽  
W. Klein ◽  
Dietrich Stauffer
Keyword(s):  
Three Dimensional ◽  
Ising Models

scholarly journals AERODYNAMICS OF JETS INTERACTING WITH A FLAT SURFACE

2019 ◽  
Vol 62 (4) ◽  
pp. 263-269
Author(s):  
I. A. Pribytkov ◽  
S. I. Kondrashenko
Keyword(s):  
Heat Transfer ◽  
Critical Point ◽  
Flat Surface ◽  
Stokes Equations ◽  
Thermal State ◽  
Exchange Process ◽  
Three Dimensional ◽  
Internal Diameter ◽  
Three Dimensional Model ◽  
Aerodynamic Properties

In this paper, the development features of a single free jet of hightemperature nitrogen interacting with a flat surface were studied. Calculation of the heat exchange process during heating by the attacking jets is very difficult to implement analytically due to complexity of the gas-dynamic processes occurring both in a single jet and in a system of jets interacting with the metal. The computational difficulties are aggravated by the fact that when interacting with the surface the jet as such disappears. The flat (fan) flow interacts with the surface: form, aerodynamic properties and thermal state of the flow strongly differ from those of the original jet. The studies were conducted on the basis of numerical simulation in the FloEFD software and computing complex for multiphysical simulation based on solution of the equations of gas dynamics and heat transfer. The solved system of equations consisted of Navier-Stokes equations, equations of energy and continuity and was supplemented by k – ε turbulence model. A three-dimensional model was developed for simulation, the necessary properties, initial and boundary conditions were specified. In the study of aerodynamics of a single high-temperature jet interacting with the surface, the main defining values were: nitrogen flow rate from the nozzle U0 , nitrogen temperature T, internal diameter of the nozzle d0 , distance from the nozzle section to the surface h, distance from the critical point (point of intersection of the jet axis with the surface) along the flow radius r. Data on the gas velocity decrease as the jet develops due to the loss of initial energy to engage the motionless surrounding gas in motion, is presented. The studies have shown that increase in the initial velocity of gas outflow brings the area of higher velocities closer to the surface both in the jet itself and in the fan jet. This factor contributes to heat transfer intensification. In addition, high speeds increase the total thickness of the fan flow and reduce the thickness of hydrodynamic boundary layer, which increases with distance from the critical point.

Determine the critical fermion flavor in three-dimensional QED using nonlocal gauge

2014 ◽  
Vol 29 (33) ◽  
pp. 1450159
Author(s):  
Hua Jiang ◽  
Yong-Long Wang ◽  
Wei-Tao Lu ◽  
Chuan-Cong Wang
Keyword(s):  
Symmetry Breaking ◽  
Critical Point ◽  
Chiral Symmetry ◽  
Gauge Boson ◽  
Quantum Electrodynamics ◽  
Chiral Symmetry Breaking ◽  
Three Dimensional ◽  
Gauge Parameter ◽  
Dynamical Chiral Symmetry Breaking

We determine the critical fermion flavor for dynamical chiral symmetry breaking in three-dimensional quantum electrodynamics using nonlocal gauge (gauge parameter depends on the momentum or coordinate). The coupled Dyson–Schwinger equations of the fermion and gauge boson propagators are considered in the vicinity of the critical point. Illustrated by using the transverse vertex proposed by Bashir et al., we show that: for a variety of the transverse vertex, the critical flavor is still 128/3π2, the same as using the bare vertex.

scholarly journals LOOPS, SURFACES AND GRASSMANN REPRESENTATION IN TWO- AND THREE-DIMENSIONAL ISING MODELS

1999 ◽  
Vol 14 (29) ◽  
pp. 4549-4574 ◽  
Author(s):  
C. R. GATTRINGER ◽  
S. JAIMUNGAL ◽  
G. W. SEMENOFF
Keyword(s):  
Three Dimensional ◽  
Ising Models ◽  
Algebraic Representation ◽  
Simple Derivation ◽  
Counting Problems ◽  
Intrinsic Geometry ◽  
Geometry Factor ◽  
Loop Expansion ◽  
Loop Surface

We construct an algebraic representation of the geometrical objects (loop and surface variables) dual to the spins in 2 and 3D Ising models. This algebraic calculus is simpler than dealing with the geometrical objects, in particular when analyzing geometry factors and counting problems. For the 2D case we give the corrected loop expansion of the free energy and the radius of convergence for this series. For the 3D case we give a simple derivation of the geometry factor which prevents overcounting of surfaces in the intrinsic geometry representation of the partition function, and find a classification of the surfaces to be summed over. For 2 and 3D we derive a compact formula for 2n-point functions in loop (surface) representation.

scholarly journals Network of Palladium-Based Nanorings Synthesized by Liquid-Phase Reduction Using DMSO-H2O: In Situ Monitoring of Structure Formation and Drying Deformation by ASEM

2020 ◽  
Vol 21 (9) ◽  
pp. 3271 ◽  
Author(s):  
Takuki Komenami ◽  
Akihiro Yoshimura ◽  
Yasunari Matsuno ◽  
Mari Sato ◽  
Chikara Sato
Keyword(s):  
Surface Tension ◽  
Liquid Phase ◽  
Aqueous Solutions ◽  
Critical Point ◽  
Synthesis Method ◽  
Three Dimensional ◽  
In Situ Monitoring ◽  
Critical Point Drying ◽  
Micrometer Size

We developed a liquid-phase synthesis method for Pd-based nanostructure, in which Pd dissolved in dimethyl sulfoxide (DMSO) solutions was precipitated using acid aqueous solution. In the development of the method, in situ monitoring using atmospheric scanning electron microscopy (ASEM) revealed that three-dimensional (3D) Pd-based nanonetworks were deformed to micrometer-size particles possibly by the surface tension of the solutions during the drying process. To avoid surface tension, critical point drying was employed to dry the Pd-based precipitates. By combining ASEM monitoring with critical point drying, the synthesis parameters were optimized, resulting in the formation of lacelike delicate nanonetworks using citric acid aqueous solutions. Precipitation using HCl acid aqueous solutions allowed formation of 500-nm diameter nanorings connected by nanowires. The 3D nanostructure formation was controllable and modifiable into various shapes using different concentrations of the Pd and Cl ions as the parameters.

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