On the uniqueness of the Invariant Equilibrium State and surface tension

Symmetric Equilibrium States and their properties under duality transformation are investigated. Necessary and sufficient conditions are derived for equilibrium states to be transformed into equilibrium states by duality. It is shown that ferromagnetic systems satisfying those conditions have correlation functions bounded by those corresponding to the (+) and free boundary conditions. It is then proved than any Invariant Equilibrium State of a ferromagnetic system is transformed into an equilibrium state by duality and is thus unique if the states defined by the (+), and free boundary conditions coincide on the symmetric algebra. The existence of surface tension between two pure phases is established.