ISSN:
0392-6737
Keywords:
Phase equilibria, phase transitions, and critical points of specific substances
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Description / Table of Contents:
Riassunto I metodi basati sul computer per campionare gli insiemi statistici generano catene di configurazioni in cui i membri che si susseguono differiscono di poco. Gli errori statistici sono determinati dal numero di configurazioni indipendenti contenute nel campione. Un trattamento quantitativo della persistenza della correlazione mostra che i primi due momenti della funzione di autocorrelazione di una variabilef lungo la catena sono collegati alla varianza aspettata del suo valore medio. Si mostra che la varianza dell'energia potenziale nell'insieme canonico è maggiore che nel microcanonico di un fattore pari al rapporto della capacità termica del sistema su quella di un gas ideale.
Abstract:
Резюме Методы, основанные на использовании вычислительной техники, для выбора статистических ансамблей порождают цепочки конфигураций, в которых последующие члены слегка отличаются. Статистические ошибки определяются числом независимых конфигураций, содержащихся в выборке. Количественное рассмотрение сохранения корреляции показывает, что первые два момента автокорреляционной функции переменнойf вдоль цепочки связаны с ожидаемым изменением ее средней величины. Показывается, что изменение потенциальной энергии в каноническом ансамбле оказывается больше, чем в микроканоническом; множитель пропорциональности равен отношению теплоемкости системы к теплоемкости идеального газа.
Notes:
Summary Computer methods for sampling statistical ensembles generate chains of configurations in which subsequent members differ only slightly. Statistical errors are determined by the number of independent configurations contained in the sample. A quantitative treatment of the persistence of correlation shows how the first two moments of the autocorrelation function of a variablef along the chain are connected with the expected variance of its mean. The variance of the potential energy in the canonical ensemble is shown be to larger than that in the microcanonical one by a factor which is the ratio of the system heat capacity to that of an ideal gas. A comparison has been made of the efficiency of Metropolis Monte Carlo (MC), the usual microcanonical molecular dynamic (MDM) and a modification of molecular dynamics for canonical ensemble sampling (MDC). The analysis is focused on three aspects: the mean square displacement of a representative point in configuration space, the persistence of correlation in the potential energyV and also in a function of interest in free-energy-difference calculations. In MDM simulations of crystalline solids, it was found thatV behaves as an «oscillatory» variable and that the variance of its mean is reduced by antithetic variations of its values.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02451293
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