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We analyze the d-dimensional Blume-Emery-Griffiths model in the disorderedregion of parameters and we show that its free energy can be explicitly writtenin term of a series which is absolutely convergent at any temperature in anunbounded portion of this region. As a byproduct we also obtain an upper boundfor the number of d-dimensional fixed polycubes of size n.

Absolute convergence of the free energy of the BEG model in the disordered region for all temperatures