  The Ising model on an infinite generic tree is defined as a thermodynamic
limit of finite systems. A detailed description of the corresponding
distribution of infinite spin configurations is given. As an application we
study the magnetization properties of such systems and prove that they exhibit
no spontaneous magnetization. Furthermore, the values of the Hausdorff and
spectral dimensions of the underlying trees are calculated and found to be,
respectively, $\bar{d}_h=2$ and $\bar{d}_s=4/3$.
