scholarly journals ON THE S MATRIX OF THE SUBLEADING MAGNETIC DEFORMATION OF THE TRICRITICAL ISING MODEL IN TWO DIMENSIONS

1992 ◽  
Vol 07 (21) ◽  
pp. 5281-5305 ◽  
Author(s):  
F. COLOMO ◽  
G. MUSSARDO ◽  
A. KOUBEK
Keyword(s):  
Ising Model ◽  
Finite Size ◽  
Numerical Data ◽  
Two Dimensions ◽  
Conformal Space ◽  
Crossing Symmetry ◽  
S Matrix ◽  
Space Approach ◽  
Good Agreement

We compute the S matrix of the tricritical Ising model perturbed by the subleading magnetic operator using Smirnov’s RSOS reduction of the Izergin-Korepin model. The massive model contains kink excitations which interpolate between two degenerate asymmetric vacua. As a consequence of the different structure of the two vacua, the crossing symmetry is implemented in a nontrivial way. We use finite-size techniques to compare our results with the numerical data obtained by the truncated conformal space approach and find good agreement.

Nanoscale Heat Transfer Modeling in Solids: Data Storage and Electronic Devices

2003 ◽  
Author(s):  
Sartaj S. Ghai ◽  
Myung S. Jhon ◽  
Cristina H. Amon ◽  
Yiao-Tee Hsia
Keyword(s):  
Heat Transfer ◽  
Data Storage ◽  
Electronic Devices ◽  
Internal Heat ◽  
Numerical Data ◽  
Computational Effort ◽  
Two Dimensions ◽  
Boltzmann Transport ◽  
Boltzmann Method ◽  
Good Agreement

Lattice Boltzmann method (LBM), is used to examine multi-length scale, confined heat conduction phenomena in solids for which sub-continuum regime is important. This paper describes the implementation of the method and its application to cases pertinent to data storage and electronic devices. Thin solid films with internal heat generation and with temperature difference across the boundaries are used as case studies to illustrate the benefits of the LBM. We compare our results with various hierarchical equations of heat transfer such as Fourier, Cattaneo, and Boltzmann transport equations, as well as with experimental and numerical data from the literature. Our results exhibit a good agreement with other methodologies in one and two dimensions, at a much lower computational effort.

scholarly journals DYNAMIC CRITICAL EXPONENTS OF THE ISING MODEL WITH MULTISPIN INTERACTIONS

2001 ◽  
Vol 15 (15) ◽  
pp. 487-496 ◽  
Author(s):  
C. S. SIMÕES ◽  
J. R. DRUGOWICH DE FELÍCIO
Keyword(s):  
Ising Model ◽  
Potts Model ◽  
Critical Exponents ◽  
Finite Size ◽  
Two Dimensions ◽  
Time Dynamics ◽  
Spin Interactions ◽  
Dynamic Exponent ◽  
Short Time ◽  
Multispin Interactions

We revisit the short-time dynamics of 2D Ising model with three spin interactions in one direction and estimate the critical exponents z, θ, β and ν. Taking properly into account the symmetry of the Hamiltonian, we obtain results completely different from those obtained by Wang et al.10 For the dynamic exponent z our result coincides with that of the 4-state Potts model in two dimensions. In addition, results for the static exponents ν and β agree with previous estimates obtained from finite size scaling combined with conformal invariance. Finally, for the new dynamic exponent θ we find a negative and close to zero value, a result also expected for the 4-state Potts model according to Okano et al.

THE SIMULATION OF THE TWO-DIMENSIONAL ISING MODEL IN THE PRESENCE OF AN EXTERNAL MAGNETIC FIELD ON THE CREUTZ CELLULAR AUTOMATON

2000 ◽  
Vol 11 (03) ◽  
pp. 561-572 ◽  
Author(s):  
B. KUTLU ◽  
M. KASAP ◽  
S. TURAN
Keyword(s):  
Magnetic Field ◽  
Ising Model ◽  
External Magnetic Field ◽  
Cellular Automaton ◽  
Critical Behavior ◽  
Finite Size ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Creutz Cellular Automaton ◽  
Good Agreement

The two-dimensional Ising model in a small external magnetic field, is simulated on the Creutz cellular automaton. The values of the static critical exponents for 0.0025 ≤ h ≤ 0.025 are estimated within the framework of the finite size scaling theory. The value of the field critical exponent is in a good agreement with its theoretical value of δ = 15. The results for 0.0025 ≤ h ≤ 0.025 are compatible with Ising critical behavior for T < Tc.

MONTE CARLO STUDIES OF THE THREE-DIMENSIONAL ISING MODEL IN EQUILIBRIUM

2001 ◽  
Vol 12 (07) ◽  
pp. 911-1009 ◽  
Author(s):  
MARTIN HASENBUSCH
Keyword(s):  
Monte Carlo ◽  
Ising Model ◽  
Monte Carlo Simulations ◽  
Three Dimensional ◽  
Finite Size ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Amplitude Ratios ◽  
Interface Tension ◽  
Monte Carlo Studies

We review Monte Carlo simulations of the Ising model and similar models in three dimensions that were performed in the last decade. Only recently, Monte Carlo simulations provide more accurate results for critical exponents than field theoretic methods, such as the ∊-expansion. These results were obtained with finite size scaling and "improved actions". In addition, we summarize Monte Carlo results for universal amplitude ratios, the interface tension, and the dimensional crossover from three to two dimensions.

scholarly journals FINITE SIZE SCALING ON THE ISING COEXISTENCE LINE

1992 ◽  
Vol 03 (05) ◽  
pp. 1119-1124
Author(s):  
SOURENDU GUPTA ◽  
A. IRBÄCK
Keyword(s):  
Free Energy ◽  
Ising Model ◽  
Finite Size ◽  
Temperature Phase ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Coexistence Line ◽  
Low Temperature Phase ◽  
Good Agreement

We report tests of finite-size scaling ansatzes in the low temperature phase of the two-dimensional Ising model. For moments of the magnetisation density, we find good agreement with the new ansatz of Borgs and Kotecký, and clear evidence of violations of the double Gaussian ansatz. We note that certain consequences of the convexity of the free energy are not adequately treated in either of these approaches.

THE TEST OF THE FINITE-SIZE SCALING RELATIONS FOR THE FIVE-DIMENSIONAL ISING MODEL ON THE CREUTZ CELLULAR AUTOMATON

1999 ◽  
Vol 10 (07) ◽  
pp. 1237-1245 ◽  
Author(s):  
N. AKTEKIN ◽  
Ş. ERKOÇ ◽  
M. KALAY
Keyword(s):  
Critical Temperature ◽  
Ising Model ◽  
Cellular Automaton ◽  
Finite Size ◽  
Scaling Relations ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Infinite Lattice ◽  
Creutz Cellular Automaton ◽  
Good Agreement

The five-dimensional Ising model is simulated on the Creutz cellular automaton using the finite-size lattices with the linear dimension 4≤L≤16. The exponents in the finite-size scaling relations for the magnetic susceptibility and the order parameter at the infinite-lattice critical temperature are computed to be 2.52(7) and 1.25(11) using 6≤L≤12, respectively, which are in very good agreement with the Monte Carlo results and with the theoretical predictions of 5/2 and 5/4. The critical temperature for the infinite lattice is found to be 8.779(8) using 8≤L≤16 which is also in very good agreement with the recent precise results.

NUMERICAL CHECK OF THE EXACT MASS SPECTRUM OF THE SCALING LIMIT OF T = Tc ISING MODEL WITH MAGNETIC FIELD

1989 ◽  
Vol 03 (18) ◽  
pp. 1375-1381 ◽  
Author(s):  
I. R. SAGDEEV ◽  
A. B. ZAMOLODCHIKOV
Keyword(s):  
Magnetic Field ◽  
Free Energy ◽  
Mass Spectrum ◽  
Ising Model ◽  
Scaling Limit ◽  
Exact Mass ◽  
Specific Free Energy ◽  
S Matrix ◽  
Good Agreement

We compute numerically the mass spectrum and the specific free energy for the T = T c Ising model with nonzero magnetic field in the scaling limit. The results are in good agreement with the proposed exact S-matrix.

NUMERICAL STUDY OF THE Q-COLOR PROBLEM ON A LATTICE

1987 ◽  
Vol 01 (01) ◽  
pp. 111-119 ◽  
Author(s):  
XIYAO CHEN ◽  
C.Y. PAN
Keyword(s):  
Numerical Study ◽  
Strong Support ◽  
Finite Size ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Zero Temperature ◽  
Color Problem ◽  
Exact Answer ◽  
Hypercubic Lattice ◽  
Good Agreement

By using the finite size extrapolation method and combined with a Monte Carlo simulation we have calculated the zero temperature entropy of the q-state Potts Antiferromagnet in two and three dimensions which is identical to the q-color problem in two and three dimensions. The model is laid on a hypercubic lattice. When q=3 (in two dimensions) the result is in good agreement with Lieb’s exact answer. When q>3 (in two and three dimensions) the results are in strong support of Mattis’ recent conjecture for the q-color problem. This method can also treat the d>3 cases without serious difficulties.

The Deformation of an Erythrocyte Under the Radiation Pressure by Optical Stretch

2006 ◽  
Vol 128 (6) ◽  
pp. 830-836 ◽  
Author(s):  
Yong-Ping Liu ◽  
Chuan Li ◽  
Kuo-Kang Liu ◽  
Alvin C. K. Lai
Keyword(s):  
Radiation Pressure ◽  
Experimental Situation ◽  
Numerical Data ◽  
Shear Stiffness ◽  
Cell Deformation ◽  
Membrane Properties ◽  
Optimization Approach ◽  
Bending Modulus ◽  
Average Shear ◽  
Good Agreement

In this paper, the mechanical properties of erythrocytes were studied numerically based upon the mechanical model originally developed by Pamplona and Calladine (ASME J. Biomech. Eng., 115, p. 149, 1993) for liposomes. The case under study is the erythrocyte stretched by a pair of laser beams in opposite directions within buffer solutions. The study aims to elucidate the effect of radiation pressure from the optical laser because up to now little is known about its influence on the cell deformation. Following an earlier study by Guck et al. (Phys. Rev. Lett., 84, p. 5451, 2000; Biophys. J., 81, p. 767, 2001), the empirical results of the radiation pressure were introduced and imposed on the cell surface to simulate the real experimental situation. In addition, an algorithm is specially designed to implement the simulation. For better understanding of the radiation pressure on the cell deformation, a large number of simulations were conducted for different properties of cell membrane. Results are first discussed parametrically and then evaluated by comparing with the experimental data reported by Guck et al. An optimization approach through minimizing the errors between experimental and numerical data is used to determine the optimal values of membrane properties. The results showed that an average shear stiffness around 4.611×10-6Nm−1, when the nondimensional ratio of shear modulus to bending modulus ranges from 10 to 300. These values are in a good agreement with those reported in literature.

scholarly journals Analytical expressions for a finite-size 2D Ising model

2017 ◽  
Vol 26 (3) ◽  
pp. 165-171 ◽  
Author(s):  
I. M. Karandashev ◽  
B. V. Kryzhanovsky ◽  
M. Yu. Malsagov
Keyword(s):  
Ising Model ◽  
Finite Size ◽  
Analytical Expressions
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