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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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View Full Document 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.
 Fall '11
 Zhigilei

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