Related papers: A Simple Method to Make the Wang-Landau Sampling C…
The 1/t Wang-Landau algorithm is analyzed from the viewpoint of execution time and accuracy when it is used in computations of the density of states of a two-dimensional Ising model. We find that the simulation results have a systematic…
We present a rigorous derivation for off-lattice implementations of the so-called "random-walk" algorithm recently introduced by Wang and Landau [PRL 86, 2050 (2001)]. Originally developed for discrete systems, the algorithm samples…
The thermodynamic properties of systems with long-range interactions is still an ongoing challenge, both from the point of view of theory as well as computer simulation. In this work we study a model system, a Coulomb gas confined inside a…
We apply the Linear Logarithmic Relaxation (LLR) method, which generalizes the Wang-Landau algorithm to quantum systems with continuous degrees of freedom, to the fermionic Hubbard model with repulsive interactions on the honeycomb lattice.…
Performance of Wang-Landau (W-L) algorithm in two continuous spin models is tested by determining the fluctuations in energy histogram. Finite size scaling is performed on a modified XY-model using different W-L sampling schemes.…
Evaluation of global thermodynamic properties, such as the entropy or the free energy, of complex systems featuring a high degree of frustration or disorder is often desirable. Nevertheless, they cannot be measured directly in standard…
We present a Monte Carlo method that efficiently computes the density of states for spin models having any number of interaction per spin. By combining a random-walk in the energy space with collective updates controlled by the…
For a second-order phase transition the critical energy range of interest is larger than the energy range covered by a canonical Monte Carlo simulation at the critical temperature. Such an extended energy range can be covered by performing…
The three-dimensional bimodal random-field Ising model is studied via a new finite temperature numerical approach. The methods of Wang-Landau sampling and broad histogram are implemented in a unified algorithm by using the N-fold version of…
Metropolis algorithm has been extensively employed for simulating a canonical ensemble and estimating macroscopic properties of a closed system at any desired temperature. A mechanical property, like energy can be calculated by averaging…
We presented an efficient algorithm, fast adaptive flat-histogram ensemble (FAFE), to estimate the density of states (DOS) and to enhance sampling in large systems. FAFE calculates the means of an arbitrary extensive variable $U$ in…
We present a new Monte Carlo algorithm based on the Stochastic Approximation Monte Carlo (SAMC) algorithm for directly calculating the density of states. The proposed method is Stochastic Approximation with a Dynamic update factor (SAD)…
The configurational density of states (CDOS) encodes all the relevant thermodynamic information contained in the interaction potentials for statistical mechanical systems. However, its explicit computation is usually a challenge for…
Flat histogram methods, such as Wang--Landau sampling, provide a means for high-throughput calculation of phase diagrams of atomistic/lattice model systems. Many parallelisation schemes with varying degrees of complexity have been proposed…
We present a new Monte Carlo algorithm that produces results of high accuracy with reduced simulational effort. Independent random walks are performed (concurrently or serially) in different, restricted ranges of energy, and the resultant…
We present a mathematical analysis of the Wang-Landau algorithm, prove its convergence, identify sources of errors and strategies for optimization. In particular, we found the histogram increases uniformly with small fluctuation after a…
We present a simple and efficient approximation scheme which greatly facilitates extension of Wang-Landau sampling (or similar techniques) in large systems for the estimation of critical behavior. The method, presented in an algorithmic…
We considered a higher-dimensional extension for the replica-exchange Wang-Landau algorithm to perform a random walk in the energy and magnetization space of the two-dimensional Ising model. This hybrid scheme combines the advantages of…
We show how the well-known Wang-Landau method can be modified to produce non-flat distributions. Through the choice of a suitable profile this can lead to an increase in efficiency for some systems. Examples for such an enhancement are…
We propose a flat-histogram Monte Carlo method to efficiently sample fractal landscapes such as escape time functions of open chaotic systems. This is achieved by using a random-walk step which depends on the height of the landscape via the…