Abstract
In Bru (2002 J. Phys. A: Math. Gen. 35 8969), we present a general method of superstabilization corresponding to the addition of the 'forward scattering' interaction to some non-superstable model. Here we complete the thermodynamic study done in this paper and we prove that the 'standard' thermodynamic behaviour of the non-superstable model is preserved in its superstabilized form in the grand-canonical ensemble. In particular, the Bose condensation phenomena persist in the new Bose gas. Moreover, this method ensures the strong equivalence for the new superstabilized model between the canonical and grand-canonical ensembles in the thermodynamic limit (Georgii H-O 1994 Probab. Theory Related Fields 99 171–95) and then it gives another way to analyse the canonical (infinite volume) Gibbs state of the first non-superstable model.