Confirmation of classical nucleation theory by Monte Carlo simulations in the 3-dimensional Ising model at low temperature

2000 ◽  
Vol 113 (5) ◽  
pp. 1976-1980 ◽  
Author(s):  
S. Wonczak ◽  
R. Strey ◽  
D. Stauffer
Keyword(s):  
Monte Carlo ◽  
Ising Model ◽  
Low Temperature ◽  
Monte Carlo Simulations ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
3 Dimensional

scholarly journals Monte Carlo Simulation of Hall Effect in n-Type GaN

1999 ◽  
Vol 4 (S1) ◽  
pp. 570-575 ◽  
Author(s):  
J.D. Albrecht ◽  
P.P. Ruden ◽  
E. Bellotti ◽  
K.F. Brennan
Keyword(s):  
Monte Carlo ◽  
Low Temperature ◽  
Monte Carlo Simulations ◽  
Acoustic Phonon ◽  
Phonon Scattering ◽  
Liquid Nitrogen Temperature ◽  
Inelastic Process ◽  
Polar Optical Phonon ◽  
Wurtzite Phase ◽  
Hall Factor

Results of Monte Carlo simulations of electron transport for wurtzite phase GaN in crossed, weak electric and magnetic fields are presented. It is found that the Hall factor, rH = μHall/μdrift, decreases monotonically as the temperature increases from 77K to 400K.The low temperature value of the Hall factor increases significantly with increasing doping concentration. The Monte Carlo simulations take into account the electron-lattice interaction through polar optical phonon scattering, deformation potential acoustic phonon scattering (treated as an inelastic process), and piezoelectric acoustic phonon scattering. Impurity scattering due to ionized and neutral donors is also included, with the latter found to be important at low temperature due to the relatively large donor binding energy which implies considerable carrier freeze-out already at liquid nitrogen temperature. The temperature dependences of the electron concentration, drift mobility, and Hall factor are calculated for donor concentrations equal to 5 × 1016 cm−3, 1017 cm−3, and 5 × 1017 cm−3. The Monte Carlo simulations are compared to classical analytical results obtained using the relaxation-time approximation, which is found to be adequate at low temperatures and sufficiently low carrier concentrations so that inelastic scattering effects due to optical phonons and degeneracy effects are negligible. The influence of dislocations on the Hall factor is discussed briefly.

The Relation Between Defects and Relaxation in Viscous Liquids

1985 ◽  
Vol 61 ◽  
Author(s):  
S. Brawer
Keyword(s):  
Computer Simulation ◽  
Monte Carlo ◽  
Ising Model ◽  
Monte Carlo Simulations ◽  
Relaxation Behavior ◽  
Atomic Diffusion ◽  
Kinetic Ising Model ◽  
Viscous Liquids ◽  
First Approximation

ABSTRACTIt is shown that defects can be identified in liquids, that they are related to atomic diffusion, and a model is described whereby defects give rise to the observed relaxation behavior of viscous liquids. A review is presented of defects in silicate and fluoroberyllate liquids, as studied by computer simulation. It is found that defects have the form of overcoordinated or undercoordinated atoms, and that atomic diffusion occurs only at the site of defects. The manner in which an Ising model can represent the detect structure of viscous liquids to a first approximation is presented. The results of Monte Carlo simulations of a 2-dimensional kinetic Ising model are described. The behavior of this model is qualitatively the same as that of viscous liquids.

scholarly journals MONTE CARLO SIMULATION OF ISING MODEL ON DIRECTED BARABASI–ALBERT NETWORK

2005 ◽  
Vol 16 (04) ◽  
pp. 585-589 ◽  
Author(s):  
MUNEER A. SUMOUR ◽  
M. M. SHABAT
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Ising Model ◽  
Monte Carlo Simulations ◽  
Characteristic Time ◽  
Spontaneous Magnetization ◽  
Zero Temperature ◽  
Different Temperatures ◽  
Large Systems ◽  
Ising Spins

The existence of spontaneous magnetization of Ising spins on directed Barabasi–Albert networks is investigated with seven neighbors, by using Monte Carlo simulations. In large systems, we see the magnetization for different temperatures T to decay after a characteristic time τ(T), which is extrapolated to diverge at zero temperature.

scholarly journals TESTS OF RANDOM NUMBER GENERATORS USING ISING MODEL SIMULATIONS

1996 ◽  
Vol 07 (03) ◽  
pp. 295-303 ◽  
Author(s):  
P. D. CODDINGTON
Keyword(s):  
Monte Carlo ◽  
Ising Model ◽  
Monte Carlo Simulations ◽  
High Performance ◽  
Large Scale ◽  
Random Number ◽  
Random Number Generators ◽  
Lattice Monte Carlo ◽  
High Performance Computers

Large-scale Monte Carlo simulations require high-quality random number generators to ensure correct results. The contrapositive of this statement is also true — the quality of random number generators can be tested by using them in large-scale Monte Carlo simulations. We have tested many commonly-used random number generators with high precision Monte Carlo simulations of the 2-d Ising model using the Metropolis, Swendsen-Wang, and Wolff algorithms. This work is being extended to the testing of random number generators for parallel computers. The results of these tests are presented, along with recommendations for random number generators for high-performance computers, particularly for lattice Monte Carlo simulations.

DYNAMICAL CRITICAL BEHAVIOR OF THE FOUR-DIMENSIONAL ISING MODEL

1996 ◽  
Vol 06 (06) ◽  
pp. 807-812 ◽  
Author(s):  
JOAN ADLER ◽  
DIETRICH STAUFFER
Keyword(s):  
Monte Carlo ◽  
Ising Model ◽  
Monte Carlo Simulations ◽  
Critical Behavior ◽  
Mean Field ◽  
Glauber Dynamics ◽  
Series Analysis ◽  
Logarithmic Corrections ◽  
Field Behavior

Monte Carlo simulations of the Glauber dynamics in the four-dimensional Ising model with up to 3124 spins agree with the theoretically expected logarithmic corrections to mean field behavior, if we assume J/kBTc = 0.14970, consistent with some series analysis.

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