Lattice cluster algorithms

Comparison to the lattice cluster algorithms of Sect. 3 shows that the SW and Wolff algorithms operate in the grand-canonical ensemble, in which the cluster moves do not conserve the magnetization (or the number of particles, in the lattice-gas interpretation), whereas the geometric cluster algorithm... 

In order to emphasize the analogy with the lattice cluster algorithms, we can also formulate a single-cluster (Wolff) variant of the geometric cluster algorithm [15,19]. 

So, how does the invaded cluster algorithm work Basically, it is just a variation of the Swendsen-Wang algorithm in which the temperature is continually adjusted to look for the critical point. The algorithm finds the fraction of links at which a percolating backbone of spins first forms across the lattice and uses this fraction to make successively better approximations to the critical temperature at each Monte Carlo step. In detail, here s how it goes ... 

Using successively an inverse Cluster Variation Method and an IMC algorithm, we determined a set of nine interactions for each alloy (for the IMC procedure, we used a lattice size of 4 24 ). For each alloy, the output from the inverse procedure has been used as an input interaction set in a direct MC simulation, in order to calculate a... 

In response, two dominant algorithms were developed initially for on-lattice spin systems [89,90]. Both revolve around determining an effective cluster of spins iteratively based on pairwise energies to construct a move type capable of overcoming the correlation problem in these systems, which were typically... 

MC simulations are performed with N = 10 molecules, each with four n.n. molecules on a 2d square lattice, at constant P and T, and with the same model parameters as for the MF analysis. To each molecules we associate a cell on a square lattice. The Wolffs algorithm is based on the definition of a cluster of variables chosen in such a way to be thermodynamically correlated." To define the Wolffs cluster, a bond index (arm) of a molecule is randomly selected this is the initial element of a stack. The cluster is grown by first checking the remaining arms of the same initial molecule if they are in the same Potts state, then they are added to the stack with probability Psame = ttiin... 

---