Scaling with a Parameter in Spin Systems near the Critical Point. I

The Hamiltonian of the form .!]{ = .!]{ 0 + )...!]{ 1 is discussed, where ). . is a parameter to change symmetry, dimensionality, or potential range. Scaling with the parameter ).. is studied for thermodynamic quantities such as the free energy. By assuming the scaled form F(s, )..) =S 2 -aF()..js<P) for the singular part of the free energy near the critical point Tc (S= (T-Tc) I