1. s = +1s = -1

5. Phase diagrams of the 1/2-spin Ising model H=0 similar to phase diagrams of fluids

6. EJERCICIO 9: except for T < T c

7. sisi (1944)

8. average field due to neighbouring spins external field effective field averaged magnetisation independent of dimensionality! Energy of i-th spin: Total energy: (factor 1/2 to avoid counting spin pairs twice) (quasi) ideal:

13. rama metaestable región inestable DOMINIOS MAGNÉTICOS

14. spinodal 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)

17. ordered

18. (J>0)

19. EJERCICIO 10 study the nature of the transition for |H| small

22. EJERCICIO 11a

23. EJERCICIO 11b

26. Stirling's approx.

28. Types of boundary conditions:

32. diverges but only at T=0

33. ... 1

37. A B A A B B A A B A B B A A B A A B A B B A B B A

38. NaF/AlF 3 mixture

40. structure of  -brass, CuZn

41. 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:

42. 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 CONSTANTS HAVE BEEN DROPPED!