Monte Carlo method for the Ising model in a transverse field

1988 ◽  
Vol 38 (7) ◽  
pp. 4712-4715 ◽  
Author(s):  
R. J. Creswick ◽  
H. A. Farach ◽  
J. M. Knight ◽  
C. P. Poole
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Ising Model ◽  
Transverse Field

Spreading Characteristics of Molecularly Thin Lubricant on Surfaces With Groove-Shaped Textures: Effects of Molecular Weight and End-Group Functionality

2003 ◽  
Vol 125 (2) ◽  
pp. 350-357 ◽  
Author(s):  
Hedong Zhang ◽  
Yasunaga Mitsuya ◽  
Maiko Yamada
Keyword(s):  
Molecular Weight ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Ising Model ◽  
Monte Carlo Simulations ◽  
Simulation Method ◽  
Solid Surfaces ◽  
The Monte Carlo Method ◽  
End Groups ◽  
End Group

Effects of molecular weight and end-group functionality on spreading of molecularly thin perfluoropolyether (PFPE) film over solid surfaces with groove-shaped textures have been studied by experiments and Monte Carlo simulations. In the experiments, lubricant spreading on a surface with groove-shaped textures was measured by making use of the phenomenon in which diffracted light weakens in the lubricant-covered region. It is found that grooves serve to accelerate spreading and this effect increases for deeper grooves, and also the accelerating rate becomes larger for a lubricant having a larger molecular weight or functional end-groups. In the simulations, the Monte Carlo method based on the Ising model was extended to enable us to evaluate the effect of molecular weight on the spreading of non-functional lubricant inside a groove. The validity of the newly developed simulation method was well confirmed from the agreement between the simulation and experimental results.

scholarly journals Monte Carlo simulation of stoquastic Hamiltonians

2015 ◽  
Vol 15 (13&14) ◽  
pp. 1122-1140
Author(s):  
Sergey Bravyi
Keyword(s):  
Monte Carlo ◽  
Ising Model ◽  
Ground State ◽  
State Energy ◽  
Transverse Field ◽  
Variable Number ◽  
Monte Carlo Algorithm ◽  
Standard Product ◽  
Ferromagnetic Ising Model ◽  
Transverse Field Ising Model

Stoquastic Hamiltonians are characterized by the property that their off-diagonal matrix elements in the standard product basis are real and non-positive. Many interesting quantum models fall into this class including the Transverse field Ising Model (TIM), the Heisenberg model on bipartite graphs, and the bosonic Hubbard model. Here we consider the problem of estimating the ground state energy of a local stoquastic Hamiltonian $H$ with a promise that the ground state of $H$ has a non-negligible correlation with some `guiding' state that admits a concise classical description. A formalized version of this problem called Guided Stoquastic Hamiltonian is shown to be complete for the complexity class $\MA$ (a probabilistic analogue of $\NP$). To prove this result we employ the Projection Monte Carlo algorithm with a variable number of walkers. Secondly, we show that the ground state and thermal equilibrium properties of the ferromagnetic TIM can be simulated in polynomial time on a classical probabilistic computer. This result is based on the approximation algorithm for the classical ferromagnetic Ising model due to Jerrum and Sinclair (1993).

Multispin Monte Carlo Method

2020 ◽  
Vol 20 (2) ◽  
pp. 212-220
Author(s):  
K.V. Makarova ◽  
◽  
A.G. Makarov ◽  
M.A. Padalko ◽  
V.S. Strongin ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Ising Model ◽  
Random Walks ◽  
State Space ◽  
Low Energy ◽  
Cluster Method ◽  
Markov Random ◽  
Statistical Equivalence ◽  
Statistical Sample

The article offers a Monte Carlo cluster method for numerically calculating a statistical sample of the state space of vector models. The statistical equivalence of subsystems in the Ising model and quasi-Markov random walks can be used to increase the efficiency of the algorithm for calculating thermodynamic means. The cluster multispin approach extends the computational capabilities of the Metropolis algorithm and allows one to find configurations of the ground and low-energy states.

CRITICAL BEHAVIOUR OF THE TRANSVERSE ISING MODEL WITH MODIFIED SURFACE EXCHANGE

2001 ◽  
Vol 15 (04) ◽  
pp. 379-384 ◽  
Author(s):  
J. M. WESSELINOWA ◽  
S. TRIMPER
Keyword(s):  
Monte Carlo ◽  
Surface Layer ◽  
Ising Model ◽  
Exchange Coupling ◽  
Three Dimensional ◽  
Transverse Field ◽  
Function Technique ◽  
Surface Phenomena ◽  
Surface Exchange ◽  
Modified Surface

Using a Green's function technique combined with the transfer-matrix method for the analysis of surface phenomena, we have studied a three-dimensional Ising model in a transverse field with a modified surface exchange coupling. The surface layer-polarization exponent is obtained as β s = 0.775 ± 0.006 which is entirely different from the bulk exponent of β = 0.317 ± 0.006. The results are in agreement with those based on renormalization group arguments and on Monte-Carlo simulations.

Simulation of an extended 3D mixed Ising model by Monte Carlo method

2020 ◽  
Vol 30 ◽  
pp. 993-997
Author(s):  
Anouar Elidrysy ◽  
Said Harir ◽  
Abdelilah Zouhair ◽  
Yahia Boughaleb
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Ising Model
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