We present a novel cluster algorithm for Monte Carlo simulations of the fully frustrated Ising model on the square lattice. The new method does not suffer from problems of metastability, and is extremely efficient even at 7-0. Our algorithm is a special case of a more general Monte Carlo simulation scheme. The general scheme unifies many cluster algorithms that were developed recently in order to accelerate Monte Carlo simulations.PACS numbers: 05.50.+q, 75.40.MgThe work of Swendsen and Wang x (SW) on acceleration of simulations of ferromagnetic Potts models opened a new field of interest in computational physics. The improved efficiency of their cluster algorithm gave hope that similar methods may be used to accelerate simulations of other systems, for which standard techniques are very inefficient. Indeed, generalizations appeared 2 " 8 soon after the work of SW was published.Clearly, one needs different cluster algorithms to accelerate simulations of different models and physical systems. A most important unsolved problem is that of simulating models with competing interactions and frustration. All known algorithms 1 " 8 become inefficient when competing interactions are introduced. They fail to identify the "correct" clusters, and in most cases almost all of the lattice ends up in the same cluster, leading to a trivial move. Thus, it is still very difficult, if not impossible, to perform simulations of spin glasses at low temperatures. Many optimization problems (e.g., the wiring problem in computer design, 9 the problem of finding the location of atoms in the unit cell of a crystal from x-ray scattering information, 10 etc.) fall into this class of models with frustration. Simulated annealing, 9 which is the most efficient method for such problems, also suffers from severe slowing down. The "replica" Monte Carlo algorithm 11 of SW improves simulations of the two-dimensional Ising spin glass, but is not as effective in other cases. For example, it is much less efficient than the algorithm we present here for the fully frustrat-ed Ising model on the square lattice.This Letter makes a first step towards solving some of the problems in the simulation of frustrated systems. We propose a novel cluster algorithm for simulating the fully frustrated Ising model on the square lattice. We show that it is extremely efficient even at r=0, and does not have metastable states; hence we move between ground states of the model without simulated annealing.The paper is organized as follows: First, we describe the algorithm in detail, and compare its performance at 7=0 to that of Metropolis et al. n We find that while typical time scales of the Metropolis algorithm diverge very strongly as a function of system size, our algorithm does not suffer from significant slowing down. Consequently, we can easily measure the dependence of the magnetic susceptibility on system size, and confirm that at 7=0 the system behaves as a ferromagnet at criticality. As we increase L, the linear size of the system, the susceptibility % diverges as ...

We present a cluster algorithm that strongly reduces critical slowing down for the SU(2) gauge theory on one time slice. The idea that underlies the new algorithm is to perform efficient flips for the signs of Polyakov loops. Ergodicity is ensured by combining it with a standard local algorithm. We show how to quantify critical slowing down for such a mixed algorithm. At the finite-temperature transition, the dynamical critical exponent z is --0.5, whereas for the purely local algorithm z = 2.

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The dynamic behavior of cluster algorithms is analyzed in the classical mean-field limit. Rigorous analytical results below T c establish that the dynamic exponent has the value z SW ϭ1 for the Swendsen-Wang algorithm and z W ϭ0 for the Wolff algorithm. An efficient Monte Carlo implementation is introduced, adapted for using these algorithms for fully connected graphs. Extensive simulations both above and below T c demonstrate scaling and evaluate the finite-size scaling function by means of a rather impressive collapse of the data.

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