Generic Ising Trees

Abstract:
The Ising model on a class of infinite random trees 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,̄dh=2 and ̄ds=4/3.