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There are two main lines running through this chapter. The first is the
consideration of distributions and how one is able to generate states of a system having a
specified distribution. Our goal is to expose simulation methods that generate states of a
system distributed consistent with a given thermodynamic ensemble. Mainly we focus on the
generation of states of a system with fixed volume, number of particles and temperature.
The second line concerns correlation. These correlation appear as temporal correlation in
the generation of states of a system. These lead to a degradation in the accuracy with
which an observable was computed. Correlation also appear as spatial correlation,
manifesting themselves often in a fractal geometry. How would you go about solving the
high dimensional integrals one has to solve in statistical physics? The ingenious answer
given by Metropolis et al was: Monte Carlo. Instead of trying to calculate these integrals
analytically, one samples the major contributions to an integral using a computational
algorithm on a computer. Since then, the Monte Carlo method and computational methods in
general have found wide spread application in statistical physics and many other areas,
not only in physics. Applications range from the simulation of liquids and solid,
elementary particles to polymers and biological systems. |
