Monte Metropolis algorithm

The main difference between the force-bias and the smart Monte Carlo methods is that the latter does not impose any limit on the displacement that m atom may undergo. The displacement in the force-bias method is limited to a cube of the appropriate size centred on the atom. However, in practice the two methods are very similar and there is often little to choose between them. In suitable cases they can be much more efficient at covering phase space and are better able to avoid bottlenecks in phase space than the conventional Metropolis Monte Carlo algorithm. The methods significantly enhance the acceptance rate of trial moves, thereby enabling Icirger moves to be made as well as simultaneous moves of more than one particle. However, the need to calculate the forces makes the methods much more elaborate, and comparable in complexity to molecular dynamics. 

We can now take one of two approaches (1) construct a probabilistic CA along lines with the Metropolis Monte Carlo algorithm outlined above (see section 7.1.3.1), or (2) define a deterministic but reversible rule consistent with the microcanonical prescription. As we shall immediately see, however, neither approach yields the expected results. 

Monte Carlo simulations were performed in 6/V-dimensional phase space, where N = 120-500 atoms [5]. The Metropolis algorithm was used with umbrella sampling. The weight density was... 

Gaussian approximation, 61 Monte Carlo simulations, 67-81 dynamics, 75-81 Metropolis algorithms, 70-71 nonequilibrium molecular dynamics, 71-74 structure profiles, 74-75 system details, 67-70... 

Metropolis algorithm, Monte Carlo heat flow simulation, 70-71 molecular dynamics, 76-81... 

In this section, the mechanics ofthe kinetic Monte Carlo algorithm (KMC) are compared to the Metropolis algorithm. ... 

The Metropolis Monte Carlo algorithm [47] simulates the evolution to thermal equilibrium of a solid for a fixed value of the temperature T. Given the current state of system, characterized by the parameters qt of the system, a move is applied by a shift of a randomly chosen parameter qi. If the energy after the move is less than the energy before, i.e. AE < 0, the move is accepted and the process continues from the new state. If, on the other hand, AE > 0, then the move may still be accepted with probability... 

In 1987, Swendsen and Wang (SW) [3] introduced a new Monte Carlo algorithm for the Ising spin model, which constituted a radical departure from the Metropolis or single-spin flip method used until then. Since the recipe is relatively straightforward, it is instructive to begin with a description of this algorithm. 

The crucial point to note is that the above average combines information about both the accepted and the rejected state of a trial move. Note that the Monte Carlo algorithm used to generate the random walk among the states n need not be the same as the one corresponding to TTnm- For instance, we could use standard Metropolis to generate the random walk, and use the S3Tnmetric rule [4]... 

The simplest Monte Carlo algorithm is the Metropolis algorithm [5] which can be outlined as follows ... 

The strategy in Variational Monte Carlo (VMC) is therefore to pick a proper form for a trial wave function based on physical insight for the particular system under study. In general, a number of parameters (oi,..., a ) will appear in the wave function to be treated as variational parameters. For any given set of a the Metropolis algorithm is used to sample the distribution... 

In the simplest Monte Carlo methods, such as the Metropolis algorithm, the probability of attempting to move to state j from state / is the same as the probability of attempting to move to state / from state J ... 

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