Absence of phase transitions in a class of integer spin systems

We exhibit a class of integer spin systems whose free energy can be written in term of an absolutely convergent series at any temperature. This class includes spin systems on ${\mathbb{Z}}^d$ interacting through infinite range pair potential polynomially decaying at large distances $r$ at a rate $1\mathrm{/}{r}^{d+\text{e}}$ with $\text{e}>0$. It also contains the Blume-Emery-Griffiths model in the disordered phase at large values of the crystal field.