The proposed scaling rules should also ensure a detailed thermodynamic balance, similar to the single-spin system. In the MC type of simulation, such a balance is realized through the proper choice of the adding probability, which is a kind of competition between energy change (caused by MC step) and thermal energy kBT. For the re-scaled system, the MC step means a collective change of all spins in a chosen super-cell. It is worth writing an explicit ΔE’ with Equation (1) using the scaling rules (5) ΔEi′=−∑jJ′ijΔS′i⋅S′j−K′i(ΔSi′^⋅ni^)2−gμBμ0Hi⋅ΔS′i+D∑jΔS′i⋅S′j−3(ΔS′i⋅eij)(S′j⋅eij)r′ij3=−n2∑jJijΔSi⋅Sj−n3Ki(ΔSi^⋅ni^)2−n3gμBμ0Hi⋅ΔSi+n3D∑jΔSi⋅Sj−3(ΔSi⋅eij)(Sj⋅eij)rij3