University of Virginia, MSE 4270/6270: Introduction to Atomistic Simulations, Leonid Zhigilei
Monte Carlo
Monte Carlo method is a common name for a wide variety of stochastic techniques.
These
techniques are based on the use of random numbers and probability statistics to investigate
problems in areas as diverse as economics, nuclear physics, and flow of traffic. In general, to call
something a "Monte Carlo" method, all you need to do is use random numbers to examine your
problem.
Materials science related examples include
¾
"classical" Monte Carlo: samples are drawn from a probability distribution, often the classical
Boltzmann distribution, to obtain thermodynamic properties or minimumenergy structures;
¾
"quantum" Monte Carlo: random walks are used to compute quantummechanical energies and
wavefunctions, often to solve electronic structure problems, using Schrödinger's equation as a
formal starting point;
¾
"volumetric" Monte Carlo: random number generators are used to generate volumes per atom
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 Fall '11
 Zhigilei
 Monte Carlo method, Metropolis Monte Carlo

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