LBan-1
In a system with degrees of freedom, the number of configurations grows exponentially with . For simplicity, consider Ising spins that take two values, , located on a lattice of size in dimensions. In this case, and the number of configurations is .
In the presence of disorder, the energy associated with a given configuration becomes a random quantity. For instance, in the Edwards-Anderson model:
where the sum runs over nearest neighbors , and the couplings are independent and identically distributed (i.i.d.) Gaussian random variables with zero mean and unit variance.
The energy of a given configuration is a random quantity because each system corresponds to a different realization of the disorder. In an experiment, this means that each of us has a different physical sample; in a numerical simulation, it means that each of us has generated a different set of couplings .