CM_Part_3

# CM_Part_3 - Metropolis Monte Carlo Detailed balance condition There are many possible choices of the W which will satisfy detailed balance Each

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University of Virginia, MSE 4270/6270: Introduction to Atomistic Simulations, Leonid Zhigilei Metropolis Monte Carlo: Detailed balance condition if U(n) > U(m) = = kT U kT U m n W n m W nm nm exp 1 exp ) ( ) ( ) 0 ( 1 ) ( ) 0 ( exp ) ( = > = nm nm nm U n m W U kT U n m W if U(n) < U(m) = = kT U kT U m n W n m W nm mn exp exp 1 ) ( ) ( Thus, the Metropolis Monte Carlo algorithm generates a new configuration n from a previous configuration m so that the transition probability W(m -> n) satisfies the detailed balance condition. There are many possible choices of the W which will satisfy detailed balance. Each choice would provide a dynamic method of generating an arbitrary probability distribution. Let us make sure that Metropolis algorithm satisfies the detailed balance condition.

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University of Virginia, MSE 4270/6270: Introduction to Atomistic Simulations, Leonid Zhigilei Metropolis Monte Carlo algorithm 1. Choose the initial configuration, calculate energy
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## This note was uploaded on 02/14/2012 for the course MSE 4270 taught by Professor Zhigilei during the Fall '11 term at UVA.

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CM_Part_3 - Metropolis Monte Carlo Detailed balance condition There are many possible choices of the W which will satisfy detailed balance Each

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