Phase transitions in free water nanoparticles. Theoretical modeling of [H2O]48 and [H2O]118

2015 ◽  
Vol 17 (16) ◽  
pp. 10532-10537 ◽  
Author(s):  
Aleš Vítek ◽  
René Kalus
Keyword(s):  
Heat Capacity ◽  
Monte Carlo ◽  
Phase Transitions ◽  
Monte Carlo Simulations ◽  
Free Water ◽  
Theoretical Modeling ◽  
Parallel Tempering ◽  
Two Dimensional ◽  
Histogram Method

Classical parallel-tempering Monte Carlo simulations of [H2O]48 and [H2O]118 have been performed in the isothermal–isobaric ensemble and a two-dimensional multiple-histogram method has been used to calculate the heat capacity of the two clusters.

scholarly journals Fighting topological freezing in the two-dimensional CPN−1 model

2018 ◽  
Vol 175 ◽  
pp. 02004 ◽  
Author(s):  
Martin Hasenbusch
Keyword(s):  
Monte Carlo ◽  
Boundary Conditions ◽  
Monte Carlo Simulations ◽  
Square Lattice ◽  
Open Boundary ◽  
Parallel Tempering ◽  
Two Dimensional ◽  
Open Boundary Conditions ◽  
Line Defect ◽  
Slowing Down

We perform Monte Carlo simulations of the CPN−1 model on the square lattice for N = 10, 21, and 41. Our focus is on the severe slowing down related to instantons. To fight this problem we employ open boundary conditions as proposed by Lüscher and Schaefer for lattice QCD. Furthermore we test the efficiency of parallel tempering of a line defect. Our results for open boundary conditions are consistent with the expectation that topological freezing is avoided, while autocorrelation times are still large. The results obtained with parallel tempering are encouraging.

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.

ON THE CALCULATION OF THE HEAT CAPACITY IN PATH INTEGRAL MONTE CARLO SIMULATIONS

1992 ◽  
Vol 03 (02) ◽  
pp. 337-346 ◽  
Author(s):  
D. MARX ◽  
P. NIELABA ◽  
K. BINDER
Keyword(s):  
Heat Capacity ◽  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Path Integral ◽  
General Relation ◽  
Absolute Magnitude ◽  
Computational Effort ◽  
Imaginary Time ◽  
Time Dimension ◽  
Path Integral Monte Carlo

In Path Integral Monte Carlo simulations the systems partition function is mapped to an equivalent classical one at the expense of a temperature-dependent Hamiltonian with an additional imaginary time dimension. As a consequence the standard relation linking the heat capacity Cv to the energy fluctuations, <E2>−<E>2, which is useful in standard classical problems with temperature-independent Hamiltonian, becomes invalid. Instead, it gets replaced by the general relation [Formula: see text] for the intensive heat capacity estimator; β being the inverse temperature and the subscript P indicates the P-fold discretization in the imaginary time direction. This heatcapacity estimator has the advantage of being based directly on the energy estimatorand thus requires no extra computational effort and is suited for extensive phase diagramstudies. As an example, numerical results are presented for a two-dimensional fluid withinternal magnetic quantum degrees of freedom. We discuss in detail origin and consequences of the excess term. Due to the subtraction of two relatively large contributions ofsimilar absolute magnitude a large statistical effort would be necessary for very accurateheat capacity estimates.

Percolation in two-dimensional quasicrystals by Monte Carlo simulations

1989 ◽  
Vol 22 (14) ◽  
pp. L705-L709 ◽  
Author(s):  
S Sakamoto ◽  
F Yonezawa ◽  
K Aoki ◽  
S Nose ◽  
M Hori
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Two Dimensional

Equilibrium and nonequilibrium models on solomon networks with two square lattices

2017 ◽  
Vol 28 (08) ◽  
pp. 1750099
Author(s):  
F. W. S. Lima
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Critical Exponent ◽  
Critical Points ◽  
Majority Vote ◽  
Universality Class ◽  
2D Systems ◽  
Two Dimensional ◽  
Critical Properties ◽  
Regular Lattices

We investigate the critical properties of the equilibrium and nonequilibrium two-dimensional (2D) systems on Solomon networks with both nearest and random neighbors. The equilibrium and nonequilibrium 2D systems studied here by Monte Carlo simulations are the Ising and Majority-vote 2D models, respectively. We calculate the critical points as well as the critical exponent ratios [Formula: see text], [Formula: see text], and [Formula: see text]. We find that numerically both systems present the same exponents on Solomon networks (2D) and are of different universality class than the regular 2D ferromagnetic model. Our results are in agreement with the Grinstein criterion for models with up and down symmetry on regular lattices.

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