ON THE ROLE OF SPECTRAL DIMENSION IN DETERMINING PHASE-TRANSITION

We have studied the phase transition of the Ising model on a family of fractals called Nice trees whose spectral dimension d(s) can take val ues greater than 2. The phase transition is shown to be the trivial ze ro-temperature one through exactly solving the free energy and the spo ntaneous magnetization of the system, and is different from that on Ca yley trees. The result is independent of d(s) of the structure and hen ce provides an example of trivial phase transition at d(s) greater tha n or equal to 2, which does not agree with the argument of Yu and Gong . It suggests that the role of d(s) in determining the phase transitio n may be complex.