A Monte Carlo Simulation of the Stillinger-Weber Model for Si-Ge Alloys

1994 ◽  
Vol 358 ◽  
Author(s):  
Mohamed Laradji ◽  
D. P. Landau ◽  
B. Dünweg
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Critical Point ◽  
Silicon Germanium ◽  
Finite Size ◽  
Universality Class ◽  
Phase Region ◽  
Scaling Analysis ◽  
Two Phase ◽  
Rich Phase

ABSTRACTThe bulk phase behavior of silicon-germanium alloys is investigated by means of a constant pressure Monte Carlo simulation of the Stillinger-Weber potential in the semi-grand-canonical ensemble. At low temperatures, Si and Ge phase separate into a Si-rich phase and a Ge-rich phase. The two-phase region is terminated by a critical point whose nature is investigated thoroughly by the multihistogram method combined with finite size scaling analysis. These results showed that the critical behavior of the alloy belongs to the mean field universality class, presumably due to the elastic degrees of freedom. We have also studied the structural properties of the mixture and found that the linear thermal expansions of both Si and Ge agree well with experiments. We also verified Végard's law above the critical point and calculated bond length distributions.

THE RESTRICTED SPIN MODEL

1990 ◽  
Vol 04 (16) ◽  
pp. 1029-1041
Author(s):  
H.A. FARACH ◽  
R.J. CRESWICK ◽  
C.P. POOLE
Keyword(s):  
Monte Carlo ◽  
Critical Temperature ◽  
Heisenberg Model ◽  
Anisotropy Parameter ◽  
Finite Size ◽  
Universality Class ◽  
Spin Model ◽  
Scaling Analysis ◽  
Finite Size Scaling ◽  
Monte Carlo Calculations

We present a novel anisotropic Heisenberg model in which the classical spin is restricted to a region of the unit sphere which depends on the value of the anisotropy parameter Δ. In the limit Δ→1, we recover the Ising model, and in the limit Δ→0, the isotopic Heisenberg model. Monte Carlo calculations are used to compare the critical temperature as a function of the anisotropy parameter for the restricted and unrestricted models, and finite-size scaling analysis leads to the conclusion that for all Δ>0 the model belongs to the Ising universality class. For small A the critical behavior is clearly seen in histograms of the transverse and longitudinal (z) components of the magnetization.

Critical exponents and the universality class of a minesweeper percolation model

2020 ◽  
Vol 31 (09) ◽  
pp. 2050129
Author(s):  
Yuqi Qing ◽  
Wen-Long You ◽  
Maoxin Liu
Keyword(s):  
Phase Transition ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Critical Exponents ◽  
Critical Density ◽  
Universality Class ◽  
Percolation Model ◽  
System Configuration ◽  
Percolation Transition ◽  
Second Order Phase Transition

We introduce a minesweeper percolation model, in which the system configuration is obtained via an automatic minesweeper process. For a variety of candidate networks with different lattice configurations, our process gives rise to a second-order phase transition. Using Monte Carlo simulation, we identify the critical points implied by giant components. A set of critical exponents are extracted to characterize the nature of the minesweeper percolation transition. The determined universality class shows a clear difference from the traditional percolation transition. A proper mine density of the minesweeper game should be set around the critical density.

Deposition of C60, C70 and C84 fullerene molecules, in benzene via a change of the fluid state, from a gas–liquid two phase region to the critical point

2011 ◽  
Vol 58 (3) ◽  
pp. 407-411 ◽  
Author(s):  
Takahiro Fukuda ◽  
Yoshihiro Katsube ◽  
Nami Watabe ◽  
Shunji Kurosu ◽  
Raymond L.D. Whitby ◽  
...  
Keyword(s):  
Critical Point ◽  
Phase Region ◽  
Two Phase ◽  
Fluid State

Finite Size Scaling of Hysteresis Behavior: Monte Carlo Simulation on DIFFOUR Model

2011 ◽  
Vol 425 (1) ◽  
pp. 72-81 ◽  
Author(s):  
Yongyut Laosiritaworn ◽  
Kanokwan Kanchiang ◽  
Rattikorn Yimnirun
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Finite Size ◽  
Finite Size Scaling ◽  
Hysteresis Behavior ◽  
Size Scaling
Sign in / Sign up

Export Citation Format

Share Document