Acceleration Algorithms in Monte Carlo Simulations in Statistical Physics

1991 ◽  
Vol 02 (01) ◽  
pp. 201-208
Author(s):  
ROBERT H. SWENDSEN
Keyword(s):  
Monte Carlo ◽  
Phase Transitions ◽  
Monte Carlo Simulations ◽  
Statistical Physics ◽  
Relaxation Times ◽  
Critical Slowing Down ◽  
Cluster Approach ◽  
New Developments ◽  
Slowing Down ◽  
Thermodynamic Phase

Monte Carlo simulations of thermodynamic phase transitions are usually hampered by long relaxation times due to the phenomenon of “critical slowing down.” Using a mapping due to Fortuin and Kasteleyn, a cluster approach to Monte Carlo simulations has been developed, which greatly reduces relaxation times, improving efficiency by up to two or three orders of magnitude. New developments and extensions of this approach are also discussed.

LATTICE SPIN MODELS AND NEW ALGORITHMS — A REVIEW OF MONTE CARLO COMPUTER SIMULATIONS

1990 ◽  
Vol 01 (01) ◽  
pp. 91-117 ◽  
Author(s):  
CLIVE F. BAILLIE
Keyword(s):  
Monte Carlo ◽  
Phase Transitions ◽  
Critical Exponent ◽  
Computer Simulations ◽  
Critical Slowing Down ◽  
Spin Models ◽  
Slowing Down ◽  
Monte Carlo Algorithms ◽  
Lattice Spin Models ◽  
New Algorithms

We review Monte Carlo computer simulations of spin models — both discrete and continuous. We explain the phenomenon of critical slowing which seriously degrades the efficiency of standard local Monte Carlo algorithms such as the Metropolis algorithm near phase transitions. We then go onto describe in detail the new algorithms which ameliorate the problem of critical slowing down, and give their dynamical critical exponent values.

Monte Carlo simulations of long-range order kinetics in B2 phases

1995 ◽  
Vol 10 (3) ◽  
pp. 591-595 ◽  
Author(s):  
K. Yaldram ◽  
V. Pierron-Bohnes ◽  
M.C. Cadeville ◽  
M.A. Khan
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Nearest Neighbor ◽  
Vacancy Concentration ◽  
Relaxation Times ◽  
Nearest Neighbors ◽  
Migration Energy ◽  
Ordering Kinetics ◽  
Migration Barriers ◽  
Temperature Dependences

The thermodynamic parameters that drive the atomic migration in B2 alloys are studied using Monte-Carlo simulations. The model is based on a vacancy jump mechanism between nearest neighbor sites, with a constant vacancy concentration. The ordering energy is described through an Ising Hamiltonian with interaction potentials between first and second nearest neighbors. Different migration barriers are introduced fur A and B atoms. The results of the simulations compare very well with those of experiments. The ordering kinetics are well described by exponential-like behaviors with two relaxation times whose temperature dependences are Arrhenius laws yielding effective migration energies. The ordering energy contributes significantly to the total migration energy.

A new approach to Monte Carlo simulations in statistical physics: Wang-Landau sampling

2004 ◽  
Vol 72 (10) ◽  
pp. 1294-1302 ◽  
Author(s):  
D. P. Landau ◽  
Shan-Ho Tsai ◽  
M. Exler
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Statistical Physics ◽  
New Approach

Phase transitions of single polymer chains and of polymer solutions: insights from Monte Carlo simulations

2008 ◽  
Vol 20 (49) ◽  
pp. 494215 ◽  
Author(s):  
K Binder ◽  
W Paul ◽  
T Strauch ◽  
F Rampf ◽  
V Ivanov ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Phase Transitions ◽  
Monte Carlo Simulations ◽  
Polymer Solutions ◽  
Polymer Chains

Superficial Phase Transitions in Nanoalloys

2011 ◽  
Vol 172-174 ◽  
pp. 658-663 ◽  
Author(s):  
Mohamed Briki ◽  
Jérôme Creuze ◽  
Fabienne Berthier ◽  
Bernard Legrand
Keyword(s):  
Phase Diagram ◽  
Monte Carlo ◽  
Phase Transitions ◽  
Monte Carlo Simulations ◽  
Bimetallic Nanoparticles ◽  
Bimodal Distribution ◽  
The Other ◽  
Nanoparticle Assembly ◽  
Interatomic Potentials ◽  
Grand Canonical

In order to build the phase diagram of Cu-Ag nanoalloys, we study a 405-atom nanoparticle by means of Monte Carlo simulations with relaxations usingN-body interatomic potentials. We focus on a range of nominal concentrations for which the cluster core remains Cu-pure and the (001) facets of the outer shell exhibit two original phenomena. Within the (N,mAg-mCu,P,T) ensemble, a structural and chemical bistability is observed, which affects all the (001) facets together. For a nanoparticle assembly, this will result in a bimodal distribution of clusters, some of them having their (001) facets Cu-rich with the usual square shape, the other ones having their (001) facets Ag-rich with a diamond shape. This bistability is replaced in the (NAg,NCu,P,T) ensemble by a continuous evolution of both the structure and the concentration of the (001) facets from Cu-rich square-shaped to Ag-rich diamond-shaped facets as the number of Ag atoms increases. For a nanoparticle assembly, this will result in an unimodal distribution of the cluster population concerning the properties of the (001) facets. This comparison between pseudo grand canonical and isothermal-isobaric results shows that the distribution of a population of bimetallic nanoparticles depends strongly on the conditions under it is elaborated.

scholarly journals Monte Carlo simulations of the γ–β, α–γ, and α–β phase transitions of nitrogen

1997 ◽  
Vol 106 (21) ◽  
pp. 8806-8813 ◽  
Author(s):  
A. Mulder ◽  
J. P. J. Michels ◽  
J. A. Schouten
Keyword(s):  
Monte Carlo ◽  
Phase Transitions ◽  
Monte Carlo Simulations ◽  
Β Phase
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