Transition ferromagnétique

T−→
M
Tc
f(T, M) = u−T s =f0(T) + 1
2a(T−Tc)M2+1 4bM4
f0(T)f0=u0−T s0a b
f(T, M)MT
MST
T < Tc1−T
Tcβ
β
f(T, M)
T > TcT < Tc
−−→
Bext
−−→
dMδwmag =−−→ Bext.−−→ dM
g∗
g
dg =−MdB −sdT
T Bext
•du =δw +δq du =cdT δqrev =T ds
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∂f
∂M T=a(T−Tc)M+bM3=Mb a b(T−Tc) + M2
T > Tc−∞ 0 +∞
Mb 0
a
b(T−Tc) + M2
∂f
∂M T
T < Tc−∞ −pa
bTc(1 −T/Tc) 0 pa bTc(1 −T/Tc) +∞
Mb 0
a
b(T−Tc) + M2
∂f
∂M T
MS=±pa
bTc(1 −T/Tc)β= 1/2
df =du −T ds −sdT =−sdT s =−∂f
∂T M=−f0
0(T)−1
2aM2
s
T < TCs=−f0
0(T)−a2
2b(Tc−T)
T > Tcs=−f0
0(T)
du =cdT =δq =T ds cv=T∂s
∂T =−f00
0(T) + a2
2bT T < Tc
=f00
0(T)T > Tca2
2bTc
du =δwmag +δq =µ0HextdM +δq
ds =δq
Text +δsc≥δq Text 0≥du −µ0HextdM −Textds =d(u−µ0HextM−Texts) = dg∗
g=u−µ0HM −T s =f−µ0HM
dg =du −µ0HdM −µ0MdH −T ds −sdT
dg =−µ0MdH −sdT
∂g
∂M T,H = 0 ⇔Bext =a(T−Tc)M+bM3