Fast Algorithm to Calculate Density of States

Abstract

An algorithm to calculate the density of states, based on the well-known Wang-Landau method, is introduced. Independent random walks are performed in different restricted ranges of energy, and the resultant density of states is modified by a function of time, F(t)=1/t, for large time. As a consequence, the calculated density of state, gm(E,t), approaches asymptotically the exact value gex(E) as 1/sqrt(t), avoiding the saturation of the error. It is also shown that the growth of the interface of the energy histogram belongs to the random deposition universality class.

5 pages, 5 figures

References in corpus (5)

• Optimizing the ensemble for equilibration in broad-histogram Monte Carlo simulations
• Wang-Landau algorithm for continuous models and joint density of states
• Performance Limitations of Flat Histogram Methods and Optimality of Wang-Landau Sampling
• Convergence and Refinement of the Wang-Landau Algorithm
• Wang-Landau Monte Carlo simulation of isotropic-nematic transition in liquid crystals

Cited by in corpus (90)

• Well-Tempered Metadynamics: A Smoothly Converging and Tunable Free-Energy Method
• Wang-Landau Algorithm: a Theoretical Analysis of the Saturation of the Error
• A generic, hierarchical framework for massively parallel Wang-Landau sampling
• Accelerated weight histogram method for exploring free energy landscapes
• Scalable replica-exchange framework for Wang-Landau sampling
• Multicritical Points and Crossover Mediating the Strong Violation of Universality: Wang-Landau Determinations in the Random-Bond $d=2$ Blume-Capel model
• Strong Violation of Critical Phenomena Universality: Wang-Landau Study of the 2d Blume-Capel Model under Bond Randomness
• Optimal Modification Factor and Convergence of the Wang-Landau Algorithm
• Analysis of the convergence of the 1/t and Wang-Landau algorithms in the calculation of multidimensional integrals
• Optimized Wang-Landau sampling of lattice polymers: Ground state search and folding thermodynamics of HP model proteins
• Phase transitions and anomalous normal state in superconductors with broken time reversal symmetry
• First-order transition features of the 3D bimodal random-field Ising model
• Large-deviation properties of the largest biconnected component for random graphs
• Improving the efficiency of extended ensemble simulations: The accelerated weight histogram method
• Parallel multicanonical study of the three-dimensional Blume-Capel model
• Wang-Landau sampling: Improving accuracy
• Critical and tricritical singularities from small-scale Monte Carlo simulations: The Blume-Capel model in two dimensions
• Adding alchemical variables to metadynamics to enhance sampling in free energy calculations
• Field-tuned order by disorder in Ising frustrated magnets with antiferromagnetic interactions
• Wang-Landau sampling: a criterion for halting the simulations
• Quenched bond randomness in marginal and non-marginal Ising spin models in 2D
• Multicanonical MCMC for Sampling Rare Events
• Ground state energy of noninteracting fermions with a random energy spectrum
• A new paradigm for petascale Monte Carlo simulation: Replica exchange Wang-Landau sampling
• Wang-Landau study of the triangular Blume-Capel ferromagnet
• Wetting and interfacial adsorption in the Blume-Capel model on the square lattice
• Enhanced sampling in generalized ensemble with large gap of sampling parameter: case study in temperature space random walk
• Difference of energy density of states in the Wang-Landau algorithm
• A mapping space Odyssey: characterising the statistical and metric properties of reduced representations of macromolecules
• First-order transitions and thermodynamic properties in the 2D Blume-Capel model: the transfer-matrix method revisited
• Performance of Wang-Landau algorithm in continuous spin models and a case study : modified XY-model
• Universality aspects of the 2d random-bond Ising and 3d Blume-Capel models
• Control of accuracy in the Wang-Landau algorithm
• Thermodynamics of the classical spin-ice model with nearest neighbour interactions using the Wang-Landau algorithm
• Complete high-precision entropic sampling
• Phase transitions, order by disorder and finite entropy in the Ising antiferromagnetic bilayer honeycomb lattice
• Estimating the Density of States of Frustrated Spin Systems
• Macroscopically constrained Wang-Landau method for systems with multiple order parameters and its application to drawing complex phase diagrams
• Convex Hulls of Random Walks in Higher Dimensions: A Large Deviation Study
• On the non-convergence of the Wang-Landau algorithms with multiple random walkers
• Monte Carlo Sampling in Fractal Landscapes
• Entropy of the diluted antiferromagnetic Ising models on the frustrated lattices using the Wang-Landau method
• Large peaks in the entropy of the diluted nearest-neighbor spin-ice model on the pyrochlore lattice in a [111] magnetic field
• Exploring new frontiers in statistical physics with a new, parallel Wang-Landau framework
• Multicanonical Sampling of the Space of States of H(2,n)-Vector Models
• Wang-Landau study of the 3D Ising model with bond disorder
• Computer simulation of two continuous spin models using Wang-Landau-Transition-Matrix Monte Carlo Algorithm
• Scaling and self-averaging in the three-dimensional random-field Ising model
• Universal cover-time distribution of heterogeneous random walks
• A portable and flexible implementation of the Wang--Landau algorithm in order to determine the Density of States
• Criticality in the randomness-induced second-order phase transition of the triangular Ising antiferromagnet with nearest- and next-nearest-neighbor interactions
• A new Wang-Landau approach to obtain phase diagrams for multicomponent alloys
• Intrinsic convergence properties of entropic sampling algorithms
• Magnetic phase transition in coupled spin-lattice systems: A replica-exchange Wang-Landau study
• Critical behavior of hard-core lattice gases: Wang-Landau sampling with adaptive windows
• Convergence of Stochastic Approximation Monte Carlo and modified Wang-Landau algorithms: Tests for the Ising model
• The Wang-Landau Algorithm as Stochastic Optimization and Its Acceleration
• Dynamic Canonical and Microcanonical Transition Matrix Analyses of Critical Behavior
• Large-deviations of the SIR model around the epidemic threshold
• Perturbation method to calculate the density of states
• Dynamically Optimized Wang-Landau Sampling with Adaptive Trial Moves and Modification Factors
• On properties of the Wang--Landau algorithm
• A Projected Entropy Controller for Transition Matrix Calculations
• Random matrix ensembles: Wang-Landau algorithm for spectral densities
• Phase Diagram of Flexible Polymers with Quenched Disordered Charged Monomers
• Comparison of the microcanonical population annealing algorithm with the Wang-Landau algorithm
• A Cluster Controller for Transition Matrix Calculations
• Classical and Quantum Gases on a Semiregular Mesh
• Thermally activated particle motion in biased correlated Gaussian disorder potentials
• Flat histogram method comparison on 2D Ising Model
• A New Monte Carlo Algorithm for Free Energy Calculation
• Semiparametric energy-based probabilistic models
• Connecting the Unstable Region of the Entropy to the Pattern of the Fisher's Zeros Map
• Large deviations of connected components in the stochastic block model
• Exploring the free energy gain of phase separation via Markov State Modeling
• Efficient sampling using Macrocanonical Monte Carlo and density of states mapping
• Residual Entropy of Ice: A Study Based on Transfer Matrices
• On the mixing time in the Wang-Landau algorithm
• Rejection-free cluster Wang-Landau algorithm for hard-core lattice gases
• Optimal parallelisation strategies for flat histogram Monte Carlo sampling
• Monte Carlo Approximation of Bayes Factors via Mixing with Surrogate Distributions
• Stochastic Approximation Monte Carlo with a Dynamic Update Factor
• Transition Matrix Cluster Algorithms
• Wang-Landau algorithm for entropic sampling of arch-based microstates in the volume ensemble of static granular packings
• Performance of Wang-Landau algorithm in lattice model of liquid crystals
• On the nature of the phase transitions in two-dimensional type II superconductors
• A Parallel Trajectory Swapping Wang - Landau Study Of The HP Protein Model
• Efficient implementation of the Wang-Landau algorithm for systems with length-scalable potential energy functions
• Almost sure convergence of the accelerated weight histogram algorithm
• Monte Carlo simulations of proteins in cages: influence of confinement on the stability of intermediate states