On the DLR equation for the two-dimensional sine–Gordon model

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Abstract
The Dobrushin–Lanford–Ruelle equation is studied in a certain space of measures in the case of two-dimensional trigonometric interactions. The uniqueness theorem extending the results of Albeverio and Hoegh-Krohn [S. Albeverio and R. Hoegh-Krohn, Commun. Math. Phys. 68, 95 (1979)] is proved. The extension is obtained by the application of some correlation inequalities of the Ginibre-type, which reduce the proof of the uniqueness of the translationally invariant, regular, tempered Gibbs states to the question on the independence of the infinite-volume free energy of the boundary conditions. The required independence is proved in this paper.