s = +1s = -1. phase diagrams of the 1/2-spin ising model h=0 similar to phase diagrams of fluids
Post on 21-Dec-2015
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V
Fp ,
N
Fp
0en 1log ,1log 3id3id
N
FNkTF
0
0 dp
N
F
N
F
exid FFF
exexid pkTppp
N
F
N
Fp exidex
N
Fp exex
average field due to neighbouring spins
external field
effective field
averaged magnetisation independent of
dimensionality!
HmJzmsHJzme BiBi 2)(Energy of i-th spin:
Total energy: HmNNJzmE B 2
2
1 (factor 1/2 to avoid counting spin pairs twice)
(quasi) ideal:
rama metaestable
rama metaestable
región inestable
región inestable
DOMINIOS MAGNÉTICOS
JzmmHB arctanh
spinodal region
nucleation region
nucleation region
nucleation kinetics:
nucleation barrier, critical domain size, growth by motion of
grain boundaries
spinodal decomposition:
instability at q=0 (long-wavelength fluctuation)
number of bonds probability of
one neighbour being A
probability of the other neighbour
being B
Now we make a mean-field approximation.
the Bragg-Williams approximation:
Entropic contribution. Favours mixing (disorder). Has minimum at x=1/2 (complete mixing) and maxima at x=0 and 1 (pure phases)
Energetic contribution. Favours segregation (order). Has minima at x=0 and 1 (pure phases) and maximum at x=1/2
AAN BB N
CONSTANTS HAVE BEEN DROPPED!