The Hamiltonian that is commonly used to represent the energy of the model when using Monte Carlo methods is H ( σ σ ) = − − J ∑ ∑ ⟨ ⟨ i j ⟩ ⟩ σ σ i σ σ j − − h ∑ ∑ j σ σ j . Furthermore, the Hamiltonian is further simplified by assuming zero external field h, since many questions that are posed to be solved using the model can be answered in absence of an external field. This leads us to the following energy equation for state σ: H ( σ σ ) = − − J ∑ ∑ ⟨ ⟨ i j ⟩ ⟩ σ σ i σ σ j . Given this Hamiltonian, quantities of interest such as the specific heat or the magnetization of the magnet at a given temperature can be calculated.