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A Guide to Monte Carlo for Statistical Mechanics: 1. Highways

  • J. P. Valleau
  • S. G. Whittington
Part of the Modern Theoretical Chemistry book series (MTC, volume 5)

Abstract

Monte Carlo techniques are methods of estimating the values of many-dimensional integrals by sampling with the help of random numbers.(1,2) It is obvious that this makes them methods appropriate to equilibrium statistical mechanics. Among the integrals of interest in classical statistical mechanics are ensemble averages of any “mechanical” quantity M(ξ),
$$\left\langle M \right\rangle =\int M\left( \xi \right)p\left( \xi \right)d\xi$$
(1)
where p(ξ) is the ensemble’s probability density function in the space of the variables ξ defining the microscopic mechanical state of the system. Conventional Monte Carlo work is concerned with the estimation of such averages for model systems, and is the subject of the present chapter.

Keywords

Markov Chain Monte Carlo Periodic Boundary Condition Transition Matrix Asymptotic Variance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Press, New York 1977

Authors and Affiliations

  • J. P. Valleau
    • 1
  • S. G. Whittington
    • 1
  1. 1.Lash Miller Chemical LaboratoriesUniversity of TorontoTorontoCanada

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