On this section, the implementation will focus on the Ising model. Lets consider a two-dimensional spin network, with L spins (lattice sites) on each side. There are naturally N = L 2 spins, and so, the phase space is discrete and is characterized by N spins, r → → = ( σ σ 1 , σ σ 2 , . . . , σ σ N ) where σ σ i ∈ ∈ { − − 1 , 1 } is the spin of each lattice site. The system's energy is given by E ( r → → ) = ∑ ∑ i = 1 N ∑ ∑ j ∈ ∈ v i z i ( 1 − − J i j σ σ i σ σ j ) , where v i z i 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.