Algorithme de Metropolis

T µ Eµ
exp −Eµ
kBT=e−βEµ
T kB
Q
<Q>=PµQµe−βEµ
Pµe−βEµ
Z
Z=X
µ
e−βEµ
21000
kBT
pµµ M

QM=PM
i=1 Qµip−1
µie−βEµi
PM
i=1 p−1
µie−βEµi
pµ=Z−1e−βEµ
QM=1
M
M
X
i=1
Qµi
P(µ→ν)
pµP(µ→ν) = pνP(ν→µ)
µ ν
ν µ
P(µ→ν)
P(ν→µ)=e−β(Eν−Eµ)
P(µ→ν) = S(µ→ν)A(µ→ν)

S
A(µ→ν)
A(ν→µ)=e−β(Eν−Eµ)
Eν> Eµ
ν µ
A(µ→ν) = e−β(Eν−Eµ)
.
∆E
.∆E <= 0
.∆E > 0x
[0,1[ x<e−β∆E
N
i ei
Eµ=
N−1
X
i=0
ei

< E >=PµEµe−βEµ
Pµe−βEµ
+1 −1
1e−β
0
β e−β
−1 +1

100