### Statistical Physics 3 October 13th, 2010

### Series 2

### The energy of the Ising model is given by:

### H = − ∑

### hi, ji

### Js _{i} s _{j} − h

### N i=1 ∑

### s _{i} . (1)

### We have also seen that the free energy per site, in the mean field approach, can be written:

### f = F

### N = − 1

### β ln 2 − 1

### β ln[cosh(β Jmz + β h)] + Jm ^{2} z/2 (2) where z is the number of nearest neighbours of every site and β = _{k} ^{1}

B