Monte Carlo with Absorbing Markov Chains: Fast Local Algorithms for Slow Dynamics

Abstract

A class of Monte Carlo algorithms which incorporate absorbing Markov chains is presented. In a particular limit, the lowest-order of these algorithms reduces to the $n$-fold way algorithm. These algorithms are applied to study the escape from the metastable state in the two-dimensional square-lattice nearest-neighbor Ising ferromagnet in an unfavorable applied field, and the agreement with theoretical predictions is very good. It is demonstrated that the higher-order algorithms can be many orders of magnitude faster than either the traditional Monte Carlo or $n$-fold way algorithms.

ReVTeX, Request 3 figures from [email protected]

References in corpus (4)

• Cluster Algorithm for Vertex Models
• A New Approach to Spin Glass Simulations
• Metastable lifetimes in a kinetic Ising model: Dependence on field and system size
• Numerical Transfer-Matrix Study of Metastability in the d=2 Ising Model

Cited by in corpus (45)

• Kinetic Activation Relaxation Technique
• Static and Dynamic Monte Carlo Simulations of Br Electrodeposition on Ag(100)
• Graph Transformation Method for Calculating Waiting Times in Markov Chains
• Automatic numerical evaluation of vacancy-mediated transport for arbitrary crystals: Onsager coefficients in the dilute limit using a Green function approach
• Multiscale Kinetic Monte-Carlo for Simulating Epitaxial Growth
• Parallelization of a Dynamic Monte Carlo Algorithm: a Partially Rejection-Free Conservative Approach
• Path Factorization Approach to Stochastic Simulations
• Metastability in the two-dimensional Ising model with free boundary conditions
• Kinetic Analysis of Discrete Path Sampling Stationary Point Databases
• A Method to Study Relaxation of Metastable Phases: Macroscopic Mean-Field Dynamics
• A projection method for statics and dynamics of lattice spin systems
• Low-temperature nucleation in a kinetic Ising model with soft stochastic dynamics
• Self-optimized construction of transition rate matrices from accelerated atomistic simulations with Bayesian uncertainty quantification
• Metastability, nucleation, and noise-enhanced stabilization out of equilibrium
• Low-temperature nucleation in a kinetic Ising model under different stochastic dynamics with local energy barriers
• Long term ordering kinetics of the two dimensional q-state Potts model
• Atomistic-Object Kinetic Monte Carlo simulations of irradiation damage in tungsten
• A variational principle for mass transport
• Competitive nucleation and the Ostwald rule in a generalized Potts model with multiple metastable phases
• Simulations of metastable decay in two- and three-dimensional models with microscopic dynamics
• Monte Carlo Simulation of Magnetization Reversal in Fe Sesquilayers on W(110)
• A Worm Algorithm for Two-Dimensional Spin Glasses
• Monte Carlo algorithms for charged lattice gases
• Time Quantified Monte Carlo Algorithm for Interacting Spin Array Micromagnetic Dynamics
• Rejection-free Monte Carlo Algorithms for Models with Continuous Degrees of Freedom
• A new time quantifiable Monte Carlo method in simulating magnetization reversal process
• Fast Simulation of Facilitated Spin Models
• Extreme Long-time Dynamic Monte Carlo Simulations
• Follow the fugitive: an application of the method of images to open dynamical systems
• Demagnetization via Nucleation of the Nonequilibrium Metastable Phase in a Model of Disorder
• Low-Temperature Long-Time Simulations of Ising Ferromagnets using the Monte Carlo with Absorbing Markov Chains method
• Advanced Dynamic Algorithms for the Decay of Metastable Phases in Discrete Spin Models: Bridging Disparate Time Scales
• Stochastic method for accommodation of equilibrating basins in kinetic Monte Carlo simulations
• Constrained Approximation of Effective Generators for Multiscale Stochastic Reaction Networks and Application to Conditioned Path Sampling
• Efficiency of Rejection-free dynamic Monte Carlo methods for homogeneous spin models, hard disk systems, and hard sphere systems
• Solving the Master Equation for Extremely Long Time Scale Calculations
• A rejection-free Monte Carlo method for the hard-disk system
• Efficiency of Rejection-Free Methods for Dynamic Monte Carlo Studies of Off-lattice Interacting Particles
• Effective dynamics for a kinetic Monte-Carlo model with slow and fast time scales
• Absorption kinetics of vacancies by cavities in Aluminum: numerical characterization of sink strengths and first-passage statistics through Krylov subspace projection and eigenvalue deflation
• Multiscale Modeling of Vacancy-Cluster Interactions and Solute Clustering Kinetics in Multicomponent Alloys
• Analytic Approximations for the Velocity of Field-Driven Ising Interfaces
• Frustrated Ising model on the honeycomb lattice: Metastability and universality
• Comparison of D-Wave Quantum Annealing and Classical Simulated Annealing for Local Minima Determination
• The generic Mott transition in the sine-Gordon model through an embedded worm algorithm