摘要:

I present some early history of Los Alamos, modern computing, and the Monte Carlo method to describe the likely context in which the Metropolis algorithm was developed and to support the special creativity of the development. I also note the scant immediate use of the algorithm over the 10 to 15 years after its development and speculate why. This sparse use however did include many seminal applications and led to many of the techniques still used today. This is the heritage enjoyed by us who today unhesitatingly use the Metropolis algorithm and the Monte Carlo method more generally, for exploring the properties of physical systems. © 2003 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1632111

出版商:AIP    

年代:1903

数据来源: AIP

摘要:

The motivations, history, and development of the Monte Carlo algorithm will be described by one of the originators. Early results on equations of state and other applications will be reviewed. © 2003 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1632112

出版商:AIP    

年代:1903

数据来源: AIP

摘要:

In a previous article [J. Phys. Chem. 21: 1087 (1953)] a prescription was given for moving from point to point in the configuration space of a system in such a way that averaging over many moves is equivalent to a canonical averaging over configuration space. The prescription is suitable for electronic machine calculations and provides the basis for calculations described elsewhere. The purpose of this paper is to provide a more rigorous proof of the method. © 2003 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1632113

出版商:AIP    

年代:1903

数据来源: AIP

ISSN:0094-243X    

DOI:10.1063/1.1632114

出版商:AIP    

年代:1903

数据来源: AIP

摘要:

A personal view of the use of the Metropolis Algorithm in statistical mechanics calculations at Los Alamos during the 1950s will be presented, based on [1] and [2]. © 2003 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1632115

出版商:AIP    

年代:1903

数据来源: AIP

摘要:

This talk will review the history of both cluster and histogram methods for Monte Carlo simulations. Cluster methods are based on the famous exact mapping by Fortuin and Kasteleyn from general Potts models onto a percolation representation. I will discuss the Swendsen‐Wang algorithm, as well as its improvement and extension to more general spin models by Wolff. The Replica Monte Carlo method further extended cluster simulations to deal with frustrated systems. The history of histograms is quite extensive, and can only be summarized briefly in this talk. It goes back at least to work by Salsburg et al. in 1959. Since then, it has been forgotten and rediscovered several times. The modern use of the method has exploited its ability to efficiently determine the location and height of peaks in various quantities, which is of prime importance in the analysis of critical phenomena. The extensions of this approach to the multiple histogram method and multicanonical ensembles have allowed information to be obtained over a broad range of parameters. Histogram simulations and analyses have become standard techniques in Monte Carlo simulations. © 2003 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1632116

出版商:AIP    

年代:1903

数据来源: AIP

摘要:

I discuss some of the historical circumstances that drove us to use the lattice as a non‐perturbative regulator. This approach has had immense success, convincingly demonstrating quark confinement and obtaining crucial properties of the strong interactions from first principles. I wrap up with some challenges for the future. © 2003 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1632117

出版商:AIP    

年代:1903

数据来源: AIP

摘要:

Metropolis simulations of all‐atom models of peptides (i.e. small proteins) are considered. Inspired by the funnel picture of Bryngelson and Wolyness, a transformation of the updating probabilities of the dihedral angles is defined, which uses probability densities from a higher temperature to improve the algorithmic performance at a lower temperature. The method is suitable for canonical as well as for generalized ensemble simulations. A simple approximation to the full transformation is tested at room temperature for Met‐Enkephalin in vacuum. Integrated autocorrelation times are found to be reduced by factors close to two and a similar improvement due to generalized ensemble methods enters multiplicatively. © 2003 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1632118

出版商:AIP    

年代:1903

数据来源: AIP

摘要:

Monte Carlo simulations always deal with systems of finite size, e.g. a d‐dimensional Ising lattice of linear dimensionL(with periodic boundary conditions) is treated. However, phase transitions occur only in the thermodynamic limit,L→ ∞, for finiteLthe transition is rounded and shifted. Hence it is a problem to locate precisely a phase transition with Monte Carlo methods, distinguish whether the transition is of first order or of second order, and characterize its properties accurately. A brief review is given how this problem is solved, both in principle and practically, by the application of finite size scaling concepts, both for critical points and for first order transitions. It will be argued that the fourth order cumulant of the “order parameter” of the transition is a particular convenient tool for locating the transition, and examples given will include systems such as unmixing of polymer blends, and Ising spin glasses. However, problems still remain for systems with phases exhibiting a power law decay of the order parameter correlations, such as the hexatic phase (if it exists) at the liquid‐solid transition of the hard disk systems. Unsolved problems also occur for systems such as Potts glasses, where a first order transition without latent heat is theoretically predicted to occur. Interesting finite size effects also occur when one simulates phase coexistence: long wavelength capillary wave‐type fluctuations of interfaces cause interfacial widths to depend in an intricate way on linear dimensions parallel and perpendicular to the interface(s); simulating liquid droplets coexisting with surrounding supersaturated gas in a finite volume an unconventional droplet evaporation transition with a (rounded) jump of the supersaturation occurs; etc. These phenomena still are the subject of current research. © 2003 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1632119

出版商:AIP    

年代:1903

数据来源: AIP

摘要:

Since its first description fifty years ago, the Metropolis Monte Carlo method has been used in a variety of different ways for the simulation of continuum quantum many‐body systems. This paper will consider some of the generalizations of the Metropolis algorithm employed in quantum Monte Carlo: Variational Monte Carlo, dynamical methods for projector monte carlo (i.e.diffusion Monte Carlo with rejection), multilevel sampling in path integral Monte Carlo, the sampling of permutations, cluster methods for lattice models, the penalty method for coupled electron‐ionic systems and the Bayesian analysis of imaginary time correlation functions. © 2003 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1632120

出版商:AIP    

年代:1903

数据来源: AIP