Some Remarks on Perturbation Theory and Phase Transition with an Application to Anisotropic Ising Model

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Abstract
A system with Hamiltonian H0 is assumed to undergo a phase transition at transition temperature T0. When a small perturbation term λH′ is added to H0, the transition temperature will depend on the coupling parameter λ and the critical indices will in general be changed. The change induced by the application of λH′ is classified into three types, and these types discussed for the cases of anisotropic Ising ferromagnets by means of thermodynamic perturbation theory and scaling law equation for spin correlation functions.