Computational Physics - Department of Physics

406 12 Random walks and the Metropolis algorithm

Initialize:

Establish an

initial state,

for example

a positionx(i)

Suggest

a moveyt

Compute ac-

ceptance ratio

A(x(i)→yt)

Generate a

uniformly

distributed

variabler

Is

A(x(i)→

yt)≥r?

Reject move:

x(i+^1 )=x(i)

Accept move:

x(i)=yt=x(i+^1 )

Last

move?

Get local

expecta-

tion values

Last

MC

step?

Collect

samples

End

yes

no

yes

yes

no

Fig. 12.7Chart flow for the Metropolis algorithm.