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Dynamic Monte Carlo method
About: Dynamic Monte Carlo method is a research topic. Over the lifetime, 13294 publications have been published within this topic receiving 371256 citations.
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TL;DR: In this paper, the Monte Carlo sampling technique is used to calculate the equilibrium thermodynamics of fluids and magnets, and the questions of convergence and accuracy of this method can be understood in terms of the dynamics of the appropriate stochastic model.
Abstract: By means of the Monte Carlo sampling technique the equilibrium thermodynamics of fluids and magnets can be calculated numerically. We show that the questions of convergence and accuracy of this method can be understood in terms of the dynamics of the appropriate stochastic model. Also, we discuss to what extent various choices of transition probabilities lead to different dynamic properties of the system. As examples of applications, we consider Ising and Heisenberg spin systems. The numerical results about the dynamic correlation functions are compared to simple approximations taken from the theory of the kinetic Ising model.
214 citations
214 citations
IBM1
TL;DR: In this paper, a particular Monte Carlo renormalization-group (MCRG) method is discussed, which is still in the early stages of development, but has a number of advantages over older methods, and has already produced excellent results for some systems of interest.
Abstract: In 1976, Ma1 made the suggestion of combining Monte Carlo (MC) computer simulations with a real-space renormalization-group (RG) analysis to calculate critical exponents at second-order phase transitions. Since then, numerous authors2–14 have presented various ways of implementing Ma's idea to produce a useful theoretical tool. In these lectures, I will discuss a particular Monte Carlo renormalization-group (MCRG) method that I and several coworkers have been using.7–14 The method is still in the early stages of development, but it has a number of advantages over older methods, and has already produced excellent results for some systems of interest.
213 citations
TL;DR: In this paper, a number of ways of calculating exact Monte Carlo p-values by sequential sampling are discussed. But, in particular, a sequential method is proposed for dealing with situations in which values can only be conveniently generated using a Markov chain, conditioned to pass through the observed data.
Abstract: SUMMARY The assessment of statistical significance by Monte Carlo simulation may be costly in computer time. This paper looks at a number of ways of calculating exact Monte Carlo p-values by sequential sampling. Such p-values are shown to have properties similar to those obtained by sampling with a fixed sample size. Both standard and generalized Monte Carlo procedures are discussed and, in particular, a sequential method is proposed for dealing with situations in which values can only be conveniently generated using a Markov chain, conditioned to pass through the observed data.
213 citations
TL;DR: In this paper, Monte Carlo methods for simulation of the dynamic behavior of surface reactions are developed, based on the chemical master equation, in a general framework which makes them applicable to a variety of models.
Abstract: Monte Carlo methods for the simulation of the dynamic behavior of surface reactions are developed, based on the chemical master equation. The methods are stated in a general framework which makes them applicable to a variety of models. Three methods are developed. A comparative analysis of the performance of the three methods, both theoretically and empirically, is included.
211 citations