EXACT RESULTS OF AT MODEL ON A SPECIAL KIND OF SIERPINSKI CARPETS

Exact results are obtained for the Ashkin-Teller model on a special Si erpinski carpet (SC). We calculate the partition function and correlat ion function with the transformation matrix method. Thus the asymptoti c behaviour of the correlation function is investigated in the Limit o f long distance. The results show that no phase transition occurs at a ny finite temperature for the finite R (the order of ramification) fra ctal, which is consistent with the conclusion of the Ising and Potts m odel.