Of Sierpinski Carpet Variable Universal

In this paper we consider the potts model on Sierpinski carpet (SC) by using an approximate bond-moving Migdal-Kadanoff real renormalisation group technique to study the universality on SC.The approximate theoretical and numerical results show that systems of almost same lacunarity L₂^m (Taguchi descreption) may belong to different universality classes. The claim that fractal dimension D,connectivity Q and lacunarity L₂^m serve as criteria for universality is called into question. What is the complete set of universality criteria on SC nedds further study.We also study the relation of fractal dimension D,connectivity Q,connectivity dimensionality D_con on and D_con .For SC, D_con=D, but it is not true for general fractal. We find that D_con may have possible relation with Q, for example, scattered cutout SC ,D_con=1+Q, but it is not true on general SC.We study the potts model on SC by using an approximate bond-moving Migdal-Kadanoff real space renormalisation technique to discuass the variation of correlation critical exponent v with D and Q, and the variation of critical exponent v with D_con and D_con.The numerical results show:for fixed D_con, v decreases as D_con decreases;for fixed D_con,v decreases as D_con increases ;for fixed D, v decreases as Q increases;however,for fixed Q,v does not variate monotonically with D.It seems that D_con is more important than Q in describing critical behaviour of SC.