scholarly journals Critical exponent ν of the Ising model in three dimensions with long-range correlated site disorder analyzed with Monte Carlo techniques

2020 ◽  
Vol 102 (17) ◽  
Author(s):  
Stanislav Kazmin ◽  
Wolfhard Janke
Keyword(s):  
Monte Carlo ◽  
Ising Model ◽  
Critical Exponent ◽  
Long Range ◽  
Three Dimensions ◽  
Monte Carlo Techniques ◽  
Site Disorder

Monte Carlo Simulation of Growth of Crystalline and Amorphous Silicon

1985 ◽  
Vol 63 ◽  
Author(s):  
Brian W. Dodson ◽  
Paul A. Taylor
Keyword(s):  
Monte Carlo ◽  
Interaction Model ◽  
Three Dimensions ◽  
Atomic Configuration ◽  
Potential Growth ◽  
Continuous Space ◽  
Monte Carlo Techniques ◽  
Stages Of Growth ◽  
Lennard Jones ◽  
Accurate Treatment

ABSTRACTThe authors have previously introduced a method, based on Monte Carlo techniques, for simulation of crystal growth processes in a continuous space. We have applied the method, initially used to simulate growth of two-dimensional Lennard-Jones systems, to treat growth of silicon in three dimensions. The interaction model for silicon is taken to be the recently introduced Stillinger-Weber (S-W) potential, which is a two- and threebody classical potential. Although the early stages of growth seem to be well modelled by the S-W potential, growth of even a single monolayer of epitaxial (111) silicon does not seem to be possible. Modifications to the S-W potential were considered, and found to be unacceptable physically. More accurate treatment of non-ideal atomic configuration energies is necessary to arrive at physically realistic growth simulations.

scholarly journals Long-range random transverse-field Ising model in three dimensions

2016 ◽  
Vol 93 (18) ◽  
Author(s):  
István A. Kovács ◽  
Róbert Juhász ◽  
Ferenc Iglói
Keyword(s):  
Ising Model ◽  
Long Range ◽  
Transverse Field ◽  
Three Dimensions ◽  
Transverse Field Ising Model

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.

Ising model critical exponent η from a criticality equation

1989 ◽  
Vol 67 (10) ◽  
pp. 946-951 ◽  
Author(s):  
B. Frank ◽  
L. Macot ◽  
K. V. Bassias ◽  
M. Danino
Keyword(s):  
Ising Model ◽  
Critical Exponent ◽  
Pair Correlation ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Square Lattice ◽  
Specific Method ◽  
Hamiltonian Methods ◽  
Order Of Magnitude

A pair-correlation function ansatz, previously used in the derivation of the Ising model critical exponent η for the square lattice from a criticality equation within the i-δ approximation, is investigated further. Various methods are used to calculate the multispin correlation functions entering the criticality equation. The calculations are extended to the three-dimensional cubic lattices. It is found that the values obtained for η are relatively insensitive to the specific method used. In two dimensions, η takes the values 0.2506 (i-δ method), 0.2471, and 0.2490 (renormalized Hamiltonian methods), thereby remaining within 1.2% of the exact value 1/4. In three dimensions, η ranges from 0.030 to 0.075, being of the same order of magnitude as the series value 0.041 ± 0.01.

scholarly journals MONTE-CARLO SIMULATIONS OF PHASE TRANSITIONS IN THE TWO-DIMENSIONAL ISING MODEL WITH LONG-RANGE CORRELATIONS

2017 ◽  
Vol 18 (9) ◽  
pp. 159-163
Author(s):  
A.A. Biryukov ◽  
Y.V. Degtyareva ◽  
M.A. Shleenkov
Keyword(s):  
Monte Carlo ◽  
Phase Transitions ◽  
Critical Temperature ◽  
Monte Carlo Method ◽  
Ising Model ◽  
Monte Carlo Simulations ◽  
Long Range ◽  
Temperature Increase ◽  
Two Dimensional ◽  
Long Range Correlations

In this article phase transitions in the modified two-dimensional Ising model with long-range correlations investigated. This model was studied with Monte-Carlo method and Metropolis algorithm. Critical temperature increase is shown in such model.

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