L-1

Spin glass Transition

Experiments

Parlare dei campioni di rame dopati con il magnesio, marino o no: trovare due figure una di suscettivita e una di calore specifico, prova della transizione termodinamica.

Edwards Anderson model

We consider for simplicity the Ising version of this model.

Ising spins takes two values $\sigma =\pm 1$ and live on a lattice of $N$ sitees $i=1,2,\ldots ,N$. The enregy is writteen as a sum between the nearest neighbours <i,j>:

$E=\sum _{<i,j>}J_{ij}\sigma _{i}\sigma _{j}$

The key point of the model proposed by Edwards and Anderson is that the couplings and i.i.d. coupling $J_{ij}$ drawn from a distribution $\pi (J_{ij})$.

It is crucial to assume that the mean value of the couplings is zero, otherwise the model displays ferro/antiferro order. We indicate the avergage over the couplings called disorder average, with an overline:

${\bar {J_{ij}}}\equiv \int dJ_{ij}\,J_{ij}\pi (J_{ij})=0$

The For simplicity we assume

$H=\sum _{ij}J_{ij}\sigma _{i}\sigma _{j}$