Implementation
On this section, the implementation will focus on the Ising model. Lets consider a 2 dimensional spin network, with L spins (lattice sites) on each side. There are naturally spins, and so, the phase space is discrete and is characterized by N spins, where is the spin of each lattice site. the system's energy is given by, where are the set of first neighborhood spins of i and J is the interaction matrix (for a ferromagnetic ising model, J is the identity matrix). The problem is stated.
On this example, the objective is to obtain and (for instance, to obtain the magnetic susceptibility of the system) since it's straightforward to generalize to other observables. According to the definition, .
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