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 an Ising model with $N$ spins $\sigma _{i}=\pm 1$ 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 (namely the average over the disorder) with an overline. In this case we have

${\bar {J_{ij}}}=0$

Hence the energy associated to a given configuration $\sigma _{i}=\pm 1$

 with zero average.

The For simplicity we assume

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