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On the linear variation of the critical temperature in the Gibbs distribution

We theoretically show that the critical temperature T c of the critical phenomena described within the Gibbs distribu- tion is varying linearly with the energetic parameters of the Hamiltonian. This kind of variation is due to the nature of the competition between the energy of the system and the energy kBT the thermic source. The change of this competition will lead to a different variation of the critical temperature. This linear variation has been reported by well-known theories of the simplest Ising model. In this study, we observe that this linearity concerns all well- known magnetic Hamiltonians formulated through spin-spin interactions. This competition has also a direct effect on the class of universalities in critical phenomena.